Category Archives: MA3160

Exercise. Let (X,Y) have joint density if and 0 otherwise. (a)  Find c that makes this a joint pdf. (b) Are X and Y independent ? (c) Compute (d) Compute Honors exercise. Let be a an exponential random variable with parameter … Continue reading →

Exercise. The average waiting time for the commuter train is 15 minutes . What is the probability that Joe will wait for more than 10 minutes, given that he has already waited for 5 minutes ? Exercise. Suppose that the … Continue reading →

Exercise.  About 10% of the population is left-handed. Use the normal distribution to approximate the probability that in a class of 150 students, (a) at least 25 of them are left-handed. (b) between 15 and 20 are left-handed. Honors Exercise. … Continue reading →

Exercise. Let X be a random variable with probability density function: f(x) =cx(5−x) 0≤x≤5, 0 otherwise. (a) What is the value of c?(b) What is the cumulative distribution function of X ? That is, find F (x) = P (X … Continue reading →

Exercise 1. Patricia receives  an average of two texts every 2 hours. If we assume that the number of texts is Poisson distributed, what is the probability that she receives five or more texts in a 9 hours period? Exercise 2. … Continue reading →

Exercise 1. Two dice are rolled. Consider the events A = {sum of two dice equals 3}, B = {sum of two dice equals 7 }, and C = {at least one of the dice shows a 1}. (a) What … Continue reading →

Exercise 1. Two dice are simultaneously rolled. For each pair of events defined below, compute if they are independent or not. (a) A1 ={thesumis7},B1 ={thefirstdielandsa3}. (b) A2 = {the sum is 9}, B2 = {the second die lands a 3}. (c) … Continue reading →

Exercise 1. Suppose that A and B are pairwise disjoint events for which P(A) = 0.3 and P(B) = 0.5.   What is the probability that B occurs but A does not?   What is the probability that neither A nor … Continue reading →

Suppose a License plate must consist of a combination of 8 numbers or letters. How many license plates are there if: there can only be letters?  the first three places are numbers and the last five are letters? the first … Continue reading →