Conside the bivariate and answer correctly

[ point Your statistics professor hands you a fair die, with each side having the same chance of boing the uppermost face. You are asked to toss the dig 7 times and count the number of times the die shows a topside of six. This count is represented by the random variable X. (a) Complete the probability distribution of X below. Use four decimals in each of your entries. X 1 2 T 0.00000367 (bj From the distribution you found in part (al, what can you say about the distribution of X7 The distribution of X is 7 # , with an mean of sixes and a standard deviation of [Enter your answers to two decimals) (c) As requested, you have tossed the die 7-times and observed X = 5 sixes. If you were to repeat the 7-tosses of this die, what is the probability you will observe at least the same number of sixes as this? Enter your answer to four decimal places. (d) Looking at your initial outcome of X = 5 and the chance of observing at least this outcome again, what does this say about the fairness of the die? Select the most appropriate answer. A. The distribution of the random variable X appears to be roughly symmetrical. B. The die appears not to be fair. X = 5 is an unusual event. C. The die appears to favor an outcome of a six. X' = 5 is an unusual event. D. The distribution of the random variable X appears to be skewed to the right. E. The die appears to be fair. X' = 5 is not an unusual event.Consider a bivariate normal population with #1 = 0, /2 = 2, 011 = 2, 622 = 1, and P12 = 0.5. (a) Write out the bivariate normal density. (b) Write out the squared generalized distance expression (x - p)'E-1(x - ) as a function of x, and x2. (c) Determine and sketch the constant-density contour that contains 50% of the probability.Consider a bivariate normal population with #1 = 0, /2 = 2, 011 = 2, 622 = 1, and P12 = 0.5. (a) Write out the bivariate normal density. (b) Write out the squared generalized distance expression (x - p)'E-1(x - ) as a function of x, and x2. (c) Determine and sketch the constant-density contour that contains 50% of the probability