Suppose X is a discrete random variable which only takes on positive integer values. For the cumulative distribution function associated with X, the following values are known:
F(13) = 0.45
F(21) = 0.49
F(28) = 0.55
F(34) = 0.6
F(41) = k
F(47) = 0.67
F(54) = 0.7
Assuming that Pr[28 < X ≤ 41] = 0.08, determine the value of k.
A. k = 0.57
B. k = 0.68
C. k = 0.63
D. k = 0.37
E. k = 0.07
Consider the experiment of a weighted coin being flipped ninety times. If flipping heads is three times as likely as the coin flipping tails, which of the following random variables would be used to count the total number of heads that are flipped?
A. B(90, 3/4)
B. B(90, 1/3)
C. B(90, 1/4)
D. B(3, 1/90)
E. B(270, 1/30)
A six-sided die is being rolled ten times. This die is weighted so that on average a 5 is rolled two out of every eleven times. Find the expected number of times a 5 will be rolled.
A. 1
B. 2
C. 5
D. 10/11
E. 20/11