2) Suppose life time (in months) of some electrical equipment follows exponential distribution with parameter 10. That is, if the lifetime is denoted by X, the density function of X is fX(t) = 10e 10t if t 0 and fX(t) = 0 if t < 0. a) Find the probability that the equipment lasts more than 6 month. b) Find the probability that the equipment lasts more than 10 months given that it is still working after 6 months. (Show all steps)

3) Suppose, you toss a coin 10 times. Tosses are independent. The probability of getting a head in a toss, P(H) = p. Let X be the total number of heads in 10 tosses. a) Write down the pmf of X. b) What kind of random variable is this. What is the expectation of X? c) Find E[X2 ] (it should be closed form as a function of p). Hint: try to use b