Question

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tocall the cumulative denaity function, or funion for x that caloulates the probabilty of the valxan all values belops). 0123 5 ) 0.02 0.22 0.36 060 0.89 0.97 Calculate the fellowing probabilities directly frem the cfi (ound to tvo decimal places (e) what is the probability mass union RK for (Round to o decimal places plx) the number of defects deviale me by 9000

Answer 1

a) The cumulative distributi on functi on of x is as follows F(x) 0 0.02 10.22 2 0.36 3 0.6 40.89 50.97 The probability that the random variable X is less than or equal to 2is P(Xs2)-F (2) 0.36 P(XS2) 0.36 The probability that the random variable X is ss than or equal to 2is P(Xs2) 036 (b) The probability that the random variable X is greater than 3 is P(X>3)1-P(XS3) 1-F (3) 1-0.6 0.4 P(X>3) 0.4 Therefore, the probability that the random variable X is greater than 3 is PiX > 3)0.4

(c) The probability that the random variable X is between 2 and 5 is F(S)-F(2) → 0.97-0.36 0.61 Therefore, the probability that the random variable X is between 2 and 5 is (d) The probability that the random variable X is between 2 and 5is 0.89 0.22 0.67 P(2 <X <5)0.67 Therefore, the probability that the random variable X is between 2 and 5 is P(2 <X <5) 0.67

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