Probability and statistics

Verify that for can serve as a pmf of a random variable X.

c) A continuous random variable X has a probability density function given by;

Find c hence compute P1 X 2.5. (4 marks)

d) Suppose the pmf of a r.v X is given by

Obtain the pmf of Y 2X2 . (4 marks)

e) A r.v X has pdf

determine the pdf of Y X4. (5 marks)

f) A random variable X has the probability distribution shown below

Find the values of the constant c hence determine the mean and variance of X. (5 marks)

g) A continuous r.v X has the pdf given by

find the value of the constant k. Also find the mean and the variance of X. (5 marks)

h) The average number of defects per wafer (defect density) is 3. The redundancy built into the design allows for up to 4 defects per wafer. What is the probability that the redundancy will not be sufficient if the defects follow a Poisson distribution? (4 marks)

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