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22 March, 15:31

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

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  1. 22 March, 18:52
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    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
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