Question

Help step by step please

1. For each of the following boxes, write the corresponding random variable and its distribution. The random variable, call it X should describe the possible values of a ticket drawn at random. Find the expected value of X by any method you like. Then find the expected value for the sum of 100 draws at random with replacement (a) 011 6 (b) -2-1 0 2 Answer (a) E[X]= 2, Expected value for 100 draws (b) E[X] = -0.25, Expected value for 100 draws = -25 = 200

Answer 1

As corresponding probability for X are not given hence we will use equal probabilities for each cases.

a) There are 4 values hence for each the probability is 1/4

x	0	1	1	6
p	1/4	1/4	1/4	1/4

$\small E(X)=\sum xp=0*\frac{1}{4}+1*\frac{1}{4}+1*\frac{1}{4}+6*\frac{1}{4}=\frac{8}{4}=2$

Hence E(x) = 2 for part a)

And expected values of 100 draws = 100*E(x) = 100*2 = 200

b)

x	-2	-1	0	2
p	1/4	1/4	1/4	1/4

$\small E(X)=\sum xp=-2*\frac{1}{4}-1*\frac{1}{4}+0*\frac{1}{4}+2*\frac{1}{4}=\frac{-1}{4}=-0.25$

Hence E(x) = -0.25 for part b)

And expected value of 100 draws = 100*E(x) = 100* (-0.25) = -25

Please comment if any doubt. thank you.