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(a) A discrete random variable X has the following probability distribution: X = x 1 2 P(X =x) k 3k 2k 5k ) Determine the value of constant k. (ii) Determine P(X 2 2).

(a) A discrete random variable X has the following probability distribution: X = x 1 2 P(X =x) k 3k 2k 5k ) Determine the value of constant k. (ii) Determine P(X 2 2).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 4 (a) A discrete random variable X has the following probability distribution: X = x 2 P(X = x) k 3k 2k 5k () Determine the value of constant k. (i) Determine P(X > 2). SX (b) A continuous p.d.f for a random variable X with function, P(x)= for 0<x<5. !! Determine: (i) the value of constant s. (i) P(x>1|x<4). (c) The probability that a resident of Senadin, Miri supports a wildlife conservation campaign is 0.6. A sample of 18 residents of Senadin, Miri is chosen at random. Given that the sample is binomial distribution, calculate the probability that: (i) exactly 9 residents support the campaign. (ii) less than 3 residents support the campaign. (d) The number of accidents occurring in a traffic light each week follows a Poisson distribution with mean 1.5. Determine the probability that: (i) less than 2 accidents occur in a particular week, (ii) more than 5 accidents occur in two weeks.
Transcribed Image Text:Question 4 (a) A discrete random variable X has the following probability distribution: X = x 2 P(X = x) k 3k 2k 5k () Determine the value of constant k. (i) Determine P(X > 2). SX (b) A continuous p.d.f for a random variable X with function, P(x)= for 0<x<5. !! Determine: (i) the value of constant s. (i) P(x>1|x<4). (c) The probability that a resident of Senadin, Miri supports a wildlife conservation campaign is 0.6. A sample of 18 residents of Senadin, Miri is chosen at random. Given that the sample is binomial distribution, calculate the probability that: (i) exactly 9 residents support the campaign. (ii) less than 3 residents support the campaign. (d) The number of accidents occurring in a traffic light each week follows a Poisson distribution with mean 1.5. Determine the probability that: (i) less than 2 accidents occur in a particular week, (ii) more than 5 accidents occur in two weeks.
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