Solve the problem quickly

1. A biased coin with probability of head P(H) = p is tossed seven times. (a) Find the probability of getting the sequence HHHHTTT, i.e. in this par- ticular order. (b) How many ways four heads and three tails can be obtained (i.e. please count the number of ways 4 H's and 3 T's can occur)? (c) Find the probability of getting exactly four heads regardless of the order. 2. Consider a discrete random variable X with the following probability mass func- tion (pmf): k 2 3 P(X = k) .2 .3 Let now Y = X2. (a) Find the distribution of Y. Please make sure to specify what values Y takes. (b) Using the distribution you obtained in (a), find E[Y]. (c) Compute Elk?P(X = k). Compare it with E[Y]. Discuss