3. Two coins are simultaneously tossed until one of them comes up a head and the other a tail. The first coin comes up a head with probability p and the second with probability q. All tosses are assumed independent. (a) Find the PMF, the expected value, and the variance of the number of tosses. (b) What is the probability that the last toss of the first coin is a head

Answers

Answer 1

Answer:

Step-by-step explanation:

From above-given information

Consider p to be the probability that the first coin comes up as head

Consider q to be the probability that the second coin comes up as tail.

Provided all tosses seems to be independent.

Then;

Let X represent no. of tosses, where X follows a geometric distribution with parameter;

p' = p(1-q) +q(1-p)

with probability mass function (pmf)

[tex]P(X = x) = ( 1 - p')^{x - 1} p'[/tex]

Thus, the mean (expected value) and the standard deviation can be computed as:

[tex]E(X) = \dfrac{1}{p'}[/tex]

[tex]\mathbf{E(X) = \dfrac{1}{p(1-q)+q(1-p)}}[/tex]

[tex]V(X) = \dfrac{1-p'}{(p')^2}[/tex]

[tex]\mathbf{V(X) = \dfrac{1-[p(1-q)+q(1-p)]}{[p(1-q)+q(1-p)]^2}}[/tex]

(b)

Suppose X represents that the first coin is head;

and Y represent the last toss

Therefore, the required probability is:

[tex]P(X|Y) = \dfrac{p(1-q)}{p'}[/tex]

[tex]P(X|Y) = \dfrac{p(1-q)}{p(1-q)+(1-p)q}[/tex]


Related Questions

5.2÷____= 0.052 please help meh :(

Answers

Answer:

The answer is 0.01 because 0.052=520   0.052 divided by 5.2=0.01

Step-by-step explanation:

URGENT Erin is taking part in a play at the community theater. The cast and crew ordered T-shirts for all the volunteers. The cost of a T-shirt is $8, and the total delivery charge is $45 per order. If the center has no more than $325 to buy T-shirts, how many T-shirts can they buy?

Answers

B is the correct answer. Less than or equal to 35 t shirts orders.

$325 - $45 delivery charge for ALL orders, = $280.
$280 divided by $8 per order is 35 t shirts.

Answer:

B is the correct answer. Less than or equal to 35 t shirts orders.

Step-by-step explanation:

what is the answer I need it urgently ​

Answers

it’s is 0.............

y = - 2x + 1
2x - 2y = 4
Solve systems of equations by substitutions

Answers

Answer:

x= 1

y= -1

Step-by-step explanation:

y=-2x+1

2x-2y=4

substitute for y

2x-2(-2x+1)=4

reduce

2x+4x-2=4

6x=6

x=1

y= -2(1)+1

y= -1

Solve the equation for all values of x in simplest form:
(x – 3)^2 = 11

Answers

X in the simplest form is 17/2

A contractor charges $35 for the installation of gutters, plus $1.50 per foot. If one installation cost $162.50, how many feet of gutter were required?

Answers

162.50-35.00=127.50
127.50/12=10.63
10.63 feet of guttering were required

The volume of this cylinder is 1751 cubic units. What is the volume of a cone that has the same base area and the sam height

Answers

Answer:

[tex]V_2 = 583.67[/tex]

Step-by-step explanation:

Given

Represent the volume of the cylinder with V1 and the cone with V2.

So:

[tex]V_1 = 1751[/tex]

Required

Find V2

The volume of a cylinder is:

[tex]V_1 = \pi r^2h[/tex]

Because the cone and the cylinder have the same base area and height, the volume of the cone is:

[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]

Substitute [tex]V_1[/tex] for [tex]\pi r^2h[/tex].

[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]

[tex]V_2 = \frac{1}{3}V_1[/tex]

Substitute 1751 for V1

[tex]V_2 = \frac{1}{3} * 1751[/tex]

[tex]V_2 = \frac{1* 1751}{3}[/tex]

[tex]V_2 = \frac{1751}{3}[/tex]

[tex]V_2 = 583.67[/tex]

The volume of the cone is 583.67 cubic units

A directed line segment starts at (1.0) and ends at (4.6), Point R partitions the segment
in the ratio of 2 to 1. What are the coordinates of point R?
(PLEASE HELP ASAP)

Answers

9514 1404 393

Answer:

  (3.4)

Step-by-step explanation:

The length of the given segment is 4.6 -1.0 = 3.6. The first portion of the division will be 2/(2+1) = 2/3 of that length, or (2/3)(3.6) = 2.4.

Then the coordinates of point R are ...

  (1.0) +(2.4) = (3.4)

__

Additional comment

We cannot tell if your coordinates are supposed to be Cartesian coordinates (1, 0) and (4, 6), or if they are points on a number line. As it happens, it makes no difference. The final answer is interpreted the same way the given coordinate points are interpreted: 3.4 on a number line or (3, 4) on a plane.

what is 250,000 divided by 12

Answers

Answer:

20833.3

Step-by-step explanation:

Answer:

tthe answer is. 20833.3

Solve the system of equations by the substitution method.
y = 4x-9
y-x=-3

A.(2, -1)
B.(-4,-7)
C.(-1,2)
D.(-7,-4)

Answers

Answer:

A. (2, -1)

Step-by-step explanation:

(4x - 9) - x = -3

3x - 9 = - 3

3x = 6

x = 2

y = 4(2) - 9

y = 8 -9

y = - 1

(2, -1)

Check

-1 - 2 = -3

Ashley rode her bicycle 29.4 miles in 4 hours. She rode the same number of miles each hour. How many miles did ride her bike in 1 hour?

Answers

7. 35
Miles per hour

Which value is an input of the function?
-14
-2
0
4

Answers

Answer:

4

Only answer on the x-axis

Answer:

It's 4.

Step-by-step explanation:

Did the  test on edge2021

I need help with this is this circumference or areas will mark you brainly if right

Answers

The question is cut off, but here are the formulas for area and circumference:

A = pi * r^2
C = 2 * pi * r

y = -2x + 2 y = 5x + 9​

Answers

X=-1 y=4 hope it helps

The ratio of boys to girls is 5 to 7 there are 45 boys in the school play how many girls are in the play

Answers

Answer:

63 girls.

Step-by-step explanation:

45 boys divided by 5= 9

9x7= 63 girls

20 points i will mark brainiest


Question 4

(08.03)


Solve the system of equations and choose the correct answer from the list of options.


x − y = 7

y = 3x + 12


Question 4 options:


1)


2 over 19 comma 2 over 33


2)


negative 2 over 19 comma negative 33 over 2


3)


negative 19 over 2 comma negative 33 over 2


4)


19 over 2 comma 33 over 2

Answers

Answer:

x = -9 1/2

y = -16 1/2

Step-by-step explanation:

x - y = 7

solve the above for 'y':  -y = 7 - x

multiple each side by -1:  y = x - 7

now both equations are in 'y=' form

x - 7 = 3x + 12

-2x - 7 = 12

-2x = 19

x = -19/2 or -9 1/2

-9.5 - y = 7

-y = 16.5

y = -16.5 or -16 1/2

                                       

Answer:

(-19/2, -33/2)

Step-by-step explanation:

HELPPSKEJSSJS THANKSSSS

Answers

Answer:

-7

Step-by-step explanation:

ASAP — PLS HELP OUT
WILL MARK BRAINLIEST AND GIVE A LOT OF POINTS

Answers

The correct answers are, length is 21 inches, and the width is 10 inches.


L=length; W=width.

L-2W=1
L=2W+1

P=2(L+W)
62in=2((2W+1)+W)
31in=3W+1
30in=3W
10in=W
The width is 10 inches.

L=2W+1=2(10in)+1=20in+1in=21in
The length is 21 inches.

Proof ;)
P=2(L+W)
62in=2(21in+10in)
62in=2(31in)
62in=62in

what is 13x25+3÷
15 please help im bad at math​

Answers

Answer:

325.2

Step-by-step explanation:

Factor 4x+16y using the gcf

Answers

The answer is 2(2x+8y)
2 x 2x=4x
2 x 8y=16y

Jack's Plumbing charges customers $100 per hour for repair jobs. A-1 Plumbing charges according to
the equation y = 75x + 50, where x = time in hours and y = cost in dollars.
Explain why A-1 Plumbing charges less than Jack's Plumbing for a 4-hour repair job.
Does A-1 Plumbing charge less than Jack's Plumbing for all repair jobs? Explain why or why not.

PLEASE HELPP

Answers

Answer:

37/3

Step-by-step explanation:


In a class of 30 students, 13 of them are boys.
What percentage of the class are girls?
Give your answer to 1 decimal place.

Answers

Answer:

56.7%

Step-by-step explanation:

30-13=17

(on a scientific calculator) 17/30=

0.56666667 x 100= 56.7 (round it up)

you can use this method everytime when trying to find a percantge.

Elliot has 4 1/3 candy bars. He gives 2/3 of a candy bar to Sara and 1/3 of a candy bar to Bill. How much does Elliot have left? (Work it out)

Answers

Answer:

10/3 or 3 1/3

Step-by-step explanation:

4 1/3= 13/3 as a mixed fraction

he gives 2/3 to sara:

13/3 - 2/2= 11/3

then he gives 1/3 to bill:

11/3-1/3= 10/3

he has 10/3 which is equal to 3 1/3

The volume of a cylinder with a radius of 3 inches and a height of 6 inches is 56.55 in? (Use V = Tt r2h.)
O True
O False
Please help

Answers

False

The volume of this cylinder is actually about 169.65

The answer is false

What absolute value represents a number greater than |0.37|

A: |-0.38|

B: |-0.35|

C: |-0.37|

D: |-0.39|

No wrong answers!

Answers

it’s going to be A and D

I need help I’m not sure if this the right answer.!

Answers

Answer:

is A

Step-by-step explanation:

00000000000000000000000000

Answer:

Its 0 because 12+ (-12) = 0

Give an example of a radical with two answers. Then solve your example. with give brainliest ong

Answers

I’m not sure what exactly your question is asking but here’s my answer:

Radical 4
This equals +2 or -2

I really hope this helped

5. What is the second step in proving by mathematical induction that for every positive integer n, 11" - 6 is divisible by
5, is true?
Let n = k. Then assume that 11" - 6 is divisible by 5.
Let n = 1. Then assume that 111 - 6 is divisible by 5.
Let n = k. Then assume that 11k+1 – 6 is divisible by 5.
O Let n = (k + 1). Then assume that 11k - 6 is divisible by 5.

NEED THIS ASAP
NEED A EXAM DONE WILL PAY

Answers

Answer:

The correct answer is A:Let n = k. Then assume that 11" - 6 is divisible by 5. sorry if im wrong but if correct pls mark brainliest

Answer:

Step-by-step explanation:

Premise:  If n is a positive integer, then 11ⁿ-6 is divisible by 5.

Let n=1.

11¹-6 = 5, so the premise is true for n=1.

Suppose the premise is true when n is an integer greater than 1,

then 11ⁿ-6 is divisible by 5.

11ⁿ⁺¹-6 = 11·11ⁿ - 6

   = (10+1)11ⁿ - 6

   = (10·11ⁿ) + (1·11ⁿ) - 6

   = (10·11ⁿ) + (11ⁿ - 6)

Both terms are divisible by 5, so 11ⁿ⁺¹-6 is divisible by 5. Therefore, the premise holds true for n+1.

Proof by induction.

Please help I need by Tomorrow!

Answers

Answer:

[tex]f(a) = 5a + 1[/tex]

[tex]f(a + h) = 5a + 5h +1[/tex]

[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x + 1[/tex]

Solving (a): f(a)

Substitute a for x in [tex]f(x) = 5x + 1[/tex]

[tex]f(a) = 5a + 1[/tex]

Solving (b): f(a + h)

Substitute a + h for x in [tex]f(x) = 5x + 1[/tex]

[tex]f(a + h) = 5(a + h) +1[/tex]

Open bracket

[tex]f(a + h) = 5a + 5h +1[/tex]

Solving (c): [tex]\frac{f(a + h) - f(a)}{h}[/tex]

In (a):

[tex]f(a) = 5a + 1[/tex]

In (b):

[tex]f(a + h) = 5a + 5h +1[/tex]

So:

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - (5a+1)}{h}[/tex]

Open bracket

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - 5a-1}{h}[/tex]

Collect Like Terms

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a- 5a+5h+1 -1}{h}[/tex]

[tex]\frac{f(a + h) - f(a)}{h} =\frac{5h}{h}[/tex]

[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]

Please answer 1 and 2 soon

Answers

Answer:

1.36+3+(32)(2)

=57

error is that 6 is the wrong answer

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