Q1 : Consider the following probability distribution function for a continuous random variable:
f(x) = 3x2 /35 -2< x < 3
= 0 elsewhere
(a) Show that this function satisfies the requirements of a probability distribution function.
(b) Calculate the expected (mean) value of x.
(c) Calculate the variance and the standard deviation of x.
Q2: In Problem 6.20, calculate the probability of the following cases:
(a) X ≤ 0.
(b) 0 < x ≤ 1.
(c) x = 2,
Q3: In the manufacturing of an electronic part, the probability of a part being defective is S% (a) What are the probabilities that, in a batch of 100 parts,
• 2 will be defective?
• 5 will be defective?
• 10 will be defective?