A game is played with a die having 11 sides numbered 1 to 11, each equally likely to turn up when the die is rolled. The player rolls the die, and wins if it stops with the uppermost face being in the set {2,6,7, 10, 11}. Let X be the random variable giving the number of wins if the die is rolled 4000000 times (i.e., 4 million times). (a) Explain why it is reasonable to assume that X has the binomial distribution. Equation Editor A. AI, BIU S x, x Styles Fant Size Words: 0 (b) Find the number of trials, the probability of a win on a single trial, the expected value of X and the standard deviation of X. In each case give your answer as an exact value - do not use decimals. Syntax advice. Enter your answers as exact values in Maple notation. You may enter expressions involving +.-. *./ and sqrt (square root) if needed, for example, (4+5* sqrt (6))/(7-8/9). Make sure you include all necessary brackets. Note that commas must not be used in large numbers, for example, type 1234567 and not 1,234,567. Answers: the number of trials is 4000000 the probability of a win is the expected value is E(X): the standard deviation is SD(X) = = (c) If the die is rolled 4000000 times, the probability that the number of wins is from 1817000 to 1820000 (inclusive) is given by a sum of the for b Pk> k-a where a, b are integers and p is an expression in the variable. Enter the values of a, b and a formula for boxes below. Syntax advice. Enter your answers as exact values in Maple notation. You may enter expressions involving +.-.*./ and sqrt (square root) if needed, for example, (4+5*sqrt (6))/(7-8/9). You may type c(x,y) for the binomial coefficient all necessary brackets. Pk in the Make sure you include Note that commas must not be used in large numbers, for example, type 1234567 and not 1,234,567. Your answer for Pk must be an exact algebraic formula involving the variable k. You can use and should the preview button next to any entry field to make sure that your syntax is correct Answers: a= b= Pk=