Suppose for a random variable X that E(X) = 5 and Var(X) = 3 . What is E((x+3) 2) ?

X is a discrete random variable with the following PMF: P(X = 1.4) = 0.25 P(X = -9.7) = 0.25 P(X = 10) = 0.5 Find the standard deviation of X.

In a hypothetical study of population dynamics, scientists have been tracking the number of rabbits and foxes on an island. The number of rabbits and foxes are determined once a year using high resolution infrared cameras and advanced computer vision methods.Each year, the number of rabbits and foxes are found to change by the following equations: $$ {\Delta}R = round( kr*R - krf*R*F ) $$ $$ {\Delta}F = round( -kf*F + kfr*R*F ) $$ where $ {\Delta}r $ and $ {\Delta} f $ are the changes in number of rabbits and foxes by the end of that year; and R and F are the population sizes at the end of the previous year. kr, krf, kf, kfr are coefficients that depend on the species of rabbits and foxes.With these dynamics, the scientists realize that one or both species can become extinct on the island. At the end of each year, if there are fewer than 2 animals of a kind, the scientists transfer rabbits and/or foxes to make sure there are at least 2 of each kind.Write a function…

A box contains three fair coins, and two trick coins that have heads on both sides.(a) What is the probability that a randomly selected coin from the box will come up heads whenflipped?   (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is theprobability that it’s one of the trick coins?   (c) Let X be the random variable that represents the number of heads when every coin in the box isflipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes,or you can remember that coin flips are independent of each other.)   (d) What is the expected number of heads when all the coins are flipped?Page 2