1. Roll two 4 sided dice. Calculate the sum of the numbers.a) What is the sample space?S=b) Let A be the event the sum is 3What is P(A);________________________c) Let B be the event the sum is less than 5.Then P(B) = ______________________d) Are A and B independent and why(not)__________________________________e) Are A and B mutually exclusive ____________________________________f) What is P(B|A) __________________________________________________2 Let X be the sum of the two dice given in question 1 above.a) Give the probability distribution function for X.xp(x)xp(x)(x-Âµ)2p(x)b) E(X) = __________________c) Variance of X = ___________d) Is the distribution symmetric about the mean?________________________sum3. Calculate the following Binomial probabilities.a) For n=10 and p=0.4P(X=6) =____________________________b) n=25 and p=0.5P(12? X?15) = __________________________c) n=200 p=0.5P(X=100) = __________________________4. Suppose I sample n=400 people and the proportion of the population who would vote for the Conservative party is assumed to be p=0.50. Let X be the number in the sample who say they would vote for the Conservative party in the sample.What is the mean and variance of X.Âµ = ________________________?2 = ____________________________What values of X fall within two standard deviations of the mean. ______________________5. If the average number of neutrinos arriving at a detector in an hour is 1:a) What is the probability that exactly 3 arrive in an hour______________________b) What is the probability that none enter in 2 hours._____________________________6. Suppose z is a standard normal random variable.a) What is P( z > -1.645 )_________________________________________________b) P( z < 1.28 ) = _________________ c) P( -1.645 < z < 1.645 )=_________________d) P( 1 < z < 2) = ______________________________7. If bars weigh on average 10 Kgs with a standard deviation of 2 Kg, thena) What is the probability that a randomly selected bar is less than 8Kg?____________b) What is the probability that a randomly selected bar is between 8 and 12 Kg.________c) What is the probability that 4 randomly selected bars have an average weight between 9 and11 kg. __________________________________ Continue to order citedessays.com/order