When X is a binomial random variable, then the probability X ≤ r successes can be found using the formula or the calculator command: binompdf(n, p, r). P(X < r) = binomcdf(n,p,r-1) P(X > r) = 1 - P(X ≤ r ) = 1 - binomcdf(n,p,r) P(X ≥ r) = 1 - P(X < r) = 1 - binomcdf(n,p,r-1)   If X is a binomial random variable, where there are 175 trials, and p = 0.057 find P(X ≥ 2)

For independent random variables X and Y, we have var(X -Y) = var(X)-var(Y ). * true False

Let X ~ N(1,2) and Y ~ N(4, 7) be independent random variables. Find the probability P(X + Y > 0):

2 (a) Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. What type of random variable is Y? What is P (Y = 3), expected number of sixes,Var(Y )? (b) Let U be the random variable that counts the number of accidents that occur at an intersection in one week. What type of random variable is U? Suppose that, on average, 2 accidents occur per week. Find P(U = 2), E(U), and V ar(U). (c) Let X be the recorded body temperature of a healthy adult in degrees Fahrenheit. What type of rv is X? Estimate its mean and standard deviation, based on your knowledge of body temperatures.