Statistics and Probability Answers

A team of 3 is to be chosen from 4girls and 6 boys in the team find the probability distribution distribution of x hence determine the mean and the variance of x

Suppose x has the pmf f(x)={kx for x=1,2,3,4

{0,elsewhere

Find the value of the constant k hence obtain the mean and the variance of x

For a discrete random variable y the probability distribution is f(y)={(5-y)/10,y=1,2,3,4

{0,elsewhere

Calculate E(y) and var(y)

A discrete random variable x ha s the probability distribution f(m)

f(m)={m/36,m=1,2,3,......8

{ 0,elsewhere

Find the mean and variance of M

1. Suppose the pmf of a random variable x is given by f(x)={1/6,for x=1,2,3,4,5,6

{0,elsewhere

Obtain the pmf of y=2x² and z=x-3

2.Let the pmf of a random variable X be given by f(x)={(x²+1)/18 for x=0,1,2,3

{0,elsewhere

determine the pmf of Y=x²+1

3.Suppose the pmf of a random variable x is given by f(x)={x/10 for x=0,1,2,3,4

{0,elsewhere

Obtain the pmf of y=|x-2|

4.Let the pmf of a random variable x be given by f(x)={(1/2)^x for x=1,2,3

{0,elsewhere

determine the pmf

y={1 if x is odd

{0 if x is even

5.Suppose the random variable x has the pmf is given by f(x)={1/6(5/6)^x for x=0,1,2,3,....

{0,elsewhere

Obtain the pmf of y=x-1

1.The pdf of a random variable x is given by f(x)={k(1-x),0<x<1 both inclusive

{0, elsewhere

Find the value of the constant k,the cdf of x and the value of m such that G(x)=1/2

2.Find the cdf of a random variable y where the pdf is given by

(a)f(x)={1/3,0<X<1 both inclusive

{1/3,2<x<4 both inclusive

{0,elsewhere

(b)f(x)={x/2,0<x<1 both inclusive

{1/2,1<x<2 both inclusive

{(3-x)/2,2<x<3 both inclusive

3.If the cdf of a random variable y is given by F(X)=1-9/y² for y>or equal to3

and F(x)=0 for y<3 find the P(X<or equal to 5),p(x>8) and the pdf of x.

1.The pdf of a continuous random variable x is given by f(x)={c/x1/2 ,0<x<4 both inclusive

{0 ,elsewhere

find the value of the constant c,the cdf of x and p(x>or equal to 1)

8.A coin is loaded so that heads is three times as likely as the tails. For 3 independent tosses of the coin find the pmf of the total number of heads realised and the probability of realizing at most 2 heads.

9.Supposse that the random variable x has a p.d.f given by f(x)={cx,0<x<1 o ,elsewhere.Find the values of the constant c hence determine m. so that p(x<or equal to m)=1/2

1.verify that f(x)=2x/k(k+1) for x=0,1,2,.....k. can serve as a pmf of a random variable x

2.A fair coin is flipped until a head appears. Let N represent the number of tosses required to realise a head. Find the pmf of N

3.The pmf of a discrete random variable X is given by p(X=x)=kx for x=1,2,3,4,5,6.

Find the value of the constant k, p(X<4) and p(3<x<6)

4.A die is loaded such the probability that of a face showing up is proportional to the face number. Determine the probability of each sample point

5.Roll a fair die and let X be the square of the show up.Write the probability distribution of x hence compute p(X<15) and p(3<x<30)

6.Let x be a random variable the number of hours observed when two dice are rolled together once. show that x is a discrete random variable.

7.For each of the following determine c so that the function can serve as a pmf of a random variable X

1. F(X)=cx for x=1,2,3,4,5
2. f(x)=cx² for x=0,1,2,...k
3. f(x)=c(1/6)^x for x=0,1,2,3,...
4. f(x)=c2^-x for x=0,1,2,....

1. A discrete random variable Y has a pmf given by p(Y=y)=c(3/4)^X for y=0,1,2,....Find the values of the constant c and p(x<3)