purple chalk, independently of previous choices. Each day she chooses white chalk with probability 0.5, yellow chalk with probability 0.4, and purple chalk with probability 0.1. (a) What is the probability that over the next 10 days she will choose white chalk 5 times, yellow chalk 4 times, and purple chalk 1 time? (b) What is the probability that over the next 10 days she will choose white chalk exactly 9 times? Exercise 6. A sandwich shop offers 8 different sandwiches. Jamey likes them a ally. Each day for lunch he picks one randomly, independently of previous choices. Salami, falafel and veggie are three of the eight types of sandwiches. During a given week of 5 days, let X be the number of times he chooses salami, Y the number of times he chooses falafel, Z the number of times he chooses veggie, and W the number of times he chooses something else. Find the joint probability mass function of (X, Y, Z, W). Identify the distribution of (X, Y, Z, W) by name.
Section 6.2
Exercise 6.5. Suppose X, Y have joint density function
V(xy+ y2), 0 < x < 1 and0<y< 1 f (x, = 0, otherwise.
(a) Check that f is a genuine joint density function. (b) Find the marginal density functions of X and Y. (c) Calculate the probability P(X < Y). (d) Calculate the expectation E[X2
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