Question

The probability distribution for the random variable x follows. x f(x) 20 0.25 26 0.14 31...

The probability distribution for the random variable x follows. x f(x) 20 0.25 26 0.14 31 0.28 36 0.33 Is this a valid probability distribution? What is the probability that x = 31 (to 2 decimals)? What is the probability that x is less than or equal to 26 (to 2 decimals)? What is the probability that x is greater than 31 (to 2 decimals)?

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Answer #1

The probability distribution for the random variable x is

x f(x)
20 0.25
26 0.14
31 0.28
36 0.33

Is this a valid probability distribution?

The sum of the probabilities is 0.25 + 0.14 + 0.28 + 0.33 = 1

As, the sum of the probabilities is 1, this is a valid probability distribution.

What is the probability that x = 31 (to 2 decimals)?

The probability that x = 31 is

P[x = 31] = 0.28

What is the probability that x is less than or equal to 26 (to 2 decimals)?

The probability that x is less than or equal to 26 is

P[x 26] = P[x = 20] + P[x = 26]

= 0.25 + 0.14 = 0.39

What is the probability that x is greater than 31 (to 2 decimals)?

The probability that x is greater than 31 is

P[x > 31] = P[x = 36] = 0.33

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