Chapter 6.1, Problem 2E

An insurance company provides customers with both auto and home insurance policies. For a particular customer, Χ is the deduction on his or her auto policy and Y is the deduction on the home policy. Possible values of Χ are K100 and K250, and for Y are K0, K100 and K200. The joint probability density function for (Χ,Y ) is given by the following table:   X Y K100 K250       K0 0.20 0.05       K100 0.10 0.15       K200 0.20 0.30         Find the probability for a randomly selected policy holder having a K100 deduction on the auto insurance and a K200 deduction on the home insurance.          Find the probability that a randomly selected policy holder has a home deduction of at least K100. Are the random variables Χ and Y independent? Explain your answer. If we look only at those insurance customers selecting the lowest auto mobile insurance deduction (K100), what is the probability that a randomly selected…

Suppose that random variable X is uniformly distributed between 6 and 28. Draw a graph of the density function, and then use it to help find the following probabilities: A. P (X > 28) = B. P(X < 11.5) = C. P(9 < X < 26) = D. P(13 < X < 30) =

For each of the following probability density functions, compute P (μ - 2σ < X < μ+ 2σ). f (x) = 6x (1 - x), 0 < x < 1, zero elsewhere. f (x) = (1/2)X, x = 1, 2, 3, ..., zero elsewhere.