Question

6. 125 pts. A discrete random variable, ,has posible resultwith the following probabilities (1) Do you expect any other results (such as Xa4) to occur? Why (not)? (2) What is the mean (or expected value) of this random variable? (Show all your work 1 4 石)ャ (3) What is the variance of this random variable? (Show all your work 3, 14 3 (4) What is the standard deviation of this random variable? (Show all your work)

Answer 1

Answer:

A) NO, this is a discrete variable and sum of all probabilities of all outcome (P(X=1)+P(X=2)+P(X=3)=1/6+2/6+3/6=1) is 1. Hence anything other than stated outcome is not possible.

B)

Expected Value E(x)=1*P(X=1)+2*P(X=2)+3*P(X=3)=1/6+4/6+9/6=14/6=2.33

C)

Variance = 1^2*P(X=1)+2^2*P(X=2)+3^2*P(X=3)- E(x)^2=1*1/6+4*2/6+9*3/6-2.333^2=0.556

D) Standard Deviation = $\sqrt{variance}=\sqrt{0.556}$ =0.7453