Chapter 5, Problem 5.19LB

Let X = b(16,- find E(4- 3x) and distribution function.

Let X be the service time which follows exponential distribution with parameter 2 = 0.2. Find the P(X > 5). 0.3679 0.0412 O 0.1345 O 0.2312 O 0.3256 O

If a variable X follows Poisson distribution with P(X = 1) = P(X = 2). Then, find P(X = 3) %3D a. 0.018 b. 0.213 c. 0.21 d. 0.18

Let X have a Poisson distribution. If , find the mode of the distribution.   Suppose Y has a uniform pdf over the interval [3,5]. Find its (1) first quartile, its (2) median, and (3) the sum of its third quartile and its ninth decile.

Suppose we are modelling the spread of a disease using the SI model on a graph of degree 3. Let p be the probability that the disease spreads across an edge. Which of the following statement is true:  If p=0.2, we get an epidemic that is likely to spread to many nodes.   If p=0.8, we get an epidemic that is likely to die out fairly quickly.   If p=0.3, the epidemic is likely to die out fairly quickly.   None of these

Please answer letters d. and e.

Let X1, X2,...X100 be the annual average temperature in Paris in the years 2001, 2002, ..., 2100,   respectively. Assume that average annual temperatures are sampled i.id. from a continuous distribution.(Note: For this problem, we assume the temperature distribution doesn't change over time. With global warming, this is not a good assumption.)A year is a record high if its average temperature is greater than those in all previous years (starting with 2001), and a record low if its average temperature islower than those in all previous years. By definition, the year 2001 is both a record high and a record low.1. In the 20 century (the years 2001 through 2100, inclusive), find the expected number of years that are either a record high or a record low.2. Let N be an r.v. representing the number of years required to get a new record high after the year 2001. Find P(N > n) for all positive integers n, and use thisto find the PMF of N.3. Check answers to parts (1) and (2).4. Explain how…

Please help with part g, d, and e

If N = 48, find tcv and use it to draw a t distribution with the rare and common zones labeled. Assume the tes is 2 tailed and alpha is set at .05