1) An elevator starts at the basement with 8 people (not including the elevator operator) and discharges them all by the time it reaches the top floor, number 6. In how many ways could the operator have perceived the people leaving the elevator if all people look alike to him? what if 8 people consisted of 5 men and 3 women and the operator could tell a man from a woman?

2) A total of 4 buses carrying 148 students from the same school arrives at football stadium. The buses carry respectively 40,33,25,50 students. One of the students is randomly selected. let X denote the number of students that were on the bus carrying this randomly selected students. one of the 4 bus drivers is also randomly selected. let Y denote the number of students on her bus. which of E[X] or E[Y] do you think is larger, why? also, compute E[X] and E[Y]

Solution Preview

At basement: 8C0 = 1ways
At first floor: 8C1 = 8ways
At second floor: 8C2 = 28 ways
At 3rd floor: ...

Solution Summary

This solution is comprised of a step by step explanation of probability concepts.

...rv's each with mean 1. Please see the attached file. This is a set of questions regarding probability, moment generating functions, and limit theorems. ...

... take the values 0, 1 and 2. Since there are only 2 sampled components and the probability of selecting a defective component is 2/10 = 0.2, the rv X follows a ...

... This provides examples of working with probabilities of independent ... a) Let denote f (x) the probability distribution of each random variable (rv) Y_k and F ...

... square root of X < 25 ) A random variable (rv), X, is ... The probability will appear in the Cell ... You can also find the same probabilities with a standard normal ...

... Let X be the rv following binomial with n ... The probability mass function binomial variable is given by P ... px (1 − p) n − x . The probabilities for different ...

... What is the probability that a lot will be rejected if ... 2) The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with pdf ...

... (b) What is the probability that a randomly chosen miniature Tootsie Roll will weigh more ... Population variance = λ = 4.5 (For a Poisson rv, mean = variance). ...

... (i) Let {Xi} be a sequence of rv's that converges in probability to a constant a. Assume that P(Xi > 0) = 1. a) Show that the sequence {Yi} defined by Yi = sqrt ...

...RV. ... variables, each being uniformly distrbuted over (0, 1). What is the joint cumulative distribution fuction of A, B, C? What is the probability that all of ...