Consider the following discrete probability distribution. x 15 22 34 40 P (X = x) 0.08 0.52 0.25 0.15

a. Is this a valid probability distribution?

c. What is the probability that the random variable X is less than 39? (Round your answer to 2 decimal places.) Probability

d. What is the probability that the random variable X is strictly between 9 and 24? (Round your answer to 2 decimal places.) Probability

e. What is the probability that the random variable X is greater than 17? (Round your answer to 2 decimal places.) Probability

Answer: a. Yes.

c. 0.85

d. 0.60

e. 0.92

Step-by-step explanation:

Given discrete probability distribution:

x 15 22 34 40

P (X = x) 0.08 0.52 0.25 0.15

a. The sum of the all probabilities in an distribution is 1.

here, Total sum = P (X = 15) + P (X=22) + P (X=34) + P (X=40)

= 0.08 + 0.52 + 0.25 + 0.15=1

∴ Yes, It is a valid probability distribution.

c. The probability that the random variable X is less than 39 : P (X<39)

= P (X = 15) + P (X=22) + P (X=34)

= 0.08 + 0.52 + 0.25 = 0.85

∴ The probability that the random variable X is less than 39 = 0.85

d. The probability that the random variable X is strictly between 9 and 24

:P (9
= 0.08 + 0.52 = 0.60

∴ The probability that the random variable X is strictly between 9 and 24=0.60

e. The probability that the random variable X is greater than 17 : P (X>17)

= P (X=22) + P (X=34) + P (X=40)

=0.52 + 0.25 + 0.15=0.92

∴ The probability that the random variable X is greater than 17=0.92