Let the pmf of a discrete random variables X be given by: Pfr-x) = x/k, (4) for

Question

Let the pmf of a discrete random variables X be given by: Pfr-x) = x/k, (4) for x-1, 2, 3 where k is a positive constant. a. Find k in order for the P(x) to be a pmf for X. b. Calculate the expected value ofX (5) Ata Suppose you buy one ticket. Assuming the random variable X represents the value of your gair (win-cost for the ticket). a. What are the possible values for X? b. Construct the probability mass function of the random variable X in tabular form. Calculate the expected value of your gain c.

Explanation / Answer

Ans:

4)a)For P(x)=x/k to be a pmf,

(1/k)+(2/k)+(3/k)=1

6/k=1

k=6

b)Expected value=1*(1/6)+2*(2/6)+3*(3/6)=(1/6)+(4/6)+(9/6)=14/6=7/3=2.33

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