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a) A merchant receives a shipment of five photocopying machines, two of which are defective. He randomly selects three of the machines and checks them for faults. Let the random variable X be number of faulty machines in his selection. Find the probability distribution of random variable X in the table form. b) Let X be the random variable with the cumulative probability distribution: F(x) 1 = { ²x³² x < 0 0

a) A merchant receives a shipment of five photocopying machines, two of which are defective. He randomly selects three of the machines and checks them for faults. Let the random variable X be number of faulty machines in his selection. Find the probability distribution of random variable X in the table form. b) Let X be the random variable with the cumulative probability distribution: F(x) 1 = { ²x³² x < 0 0

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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a) A merchant receives a shipment of five photocopying machines, two of which are defective. He randomly selects three of the machines and checks them for faults. Let the random variable X be number of faulty machines in his selection. Find the probability distribution of random variable X in the table form. b) Let X be the random variable with the cumulative probability distribution: 0, x < 0 F(x): = kx², 0≤x < 2 1, x ≥ 2 Determine the value of k. c) Let X be the random variable with the cumulative probability distribution: F(x) = {₁ - e-²x ¦ x < 0 x ≥ 0 Determine the expected value of X. d) The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X= 2).
Transcribed Image Text:a) A merchant receives a shipment of five photocopying machines, two of which are defective. He randomly selects three of the machines and checks them for faults. Let the random variable X be number of faulty machines in his selection. Find the probability distribution of random variable X in the table form. b) Let X be the random variable with the cumulative probability distribution: 0, x < 0 F(x): = kx², 0≤x < 2 1, x ≥ 2 Determine the value of k. c) Let X be the random variable with the cumulative probability distribution: F(x) = {₁ - e-²x ¦ x < 0 x ≥ 0 Determine the expected value of X. d) The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X= 2).
e) A recent survey indicates that 7% of all motor bikes manufactured at Baloyi factory have defective lights. A certain company from Polokwane buys ten motor bikes from this factory. What is the probability that at least two bikes have defective lights?
Transcribed Image Text:e) A recent survey indicates that 7% of all motor bikes manufactured at Baloyi factory have defective lights. A certain company from Polokwane buys ten motor bikes from this factory. What is the probability that at least two bikes have defective lights?
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