(Solved): Problem 9 Short answer (8 points) In each case, show your work/code. (a) A random variable \( X \) ...

Problem 9 Short answer (8 points) In each case, show your work/code. (a) A random variable \( X \) is binomially distributed with \( n=50 \) and \( p=0.3 \). Find the [3] probability that \( X<10 \). (b) A random variable \( T \) is exponentially distributed with a rate parameter of \( \lambda=20 \) [2] occurrences/minute. What is the mean of \( T \) ? (c) In how many ways can you have 3 successes out of 10 trials in which the outcome of [3] each trial is either success or failure?