A discrete random variable x has two possible values 5 and 1

A discrete random variable x has two possible values, 5 and 10.

P(x)= cx

a) Find c

b) What is the probability of x being equal to 3?

d) what is the probability of x being equal to 5?

Solution

a)

As P(X) = cx

Then

P(5) = 5c
P(10) = 10c

Thus,

P(5) + P(10) = 1

5c + 10c = 1

15c = 1

c = 1/15 = 0.066666667 [ANSWER]

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b)

x can only be 5 or 10. Thus,

P(3) = 0 [ANSWER]

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c)

P(5) = c*5 = 0.066666667*5 = 0.33333333 [ANSWER]