7.Suppose that the scores on a certain national test are ap-proximately normally distributed, with a mean of 570 and a standarddeviation of 20. In order to enter University ABC, a student must scoreat least 595 on this national test. Let X denote the national test scoreof a randomly selected student applicant to University ABC.What is the moment generating function M(t) of X?(a)No work is required in this part.(b)applicant will be one that is not admitted to University ABC?What is the probability that a randomly selected student

Answered: 7. Suppose that the scores on a certain…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1, (which is identical to a standard gamma distribution with α = 1), compute the following. (If necessary, round your answer to three decimal places.) (a) The expected time between two successive arrivals (b) The standard deviation of the time between successive arrivals (c) P(X ≤ 1) (d) P(1 ≤ x ≤ 3) You may need to use the appropriate table in the Appendix of Tables
. For the LOGLOGIS(4, 7) distribution with cdf [log(t)- M F(t) = Piogis :> 0; -x 0. (a) Find the probability scales that will linearize all the cdfs in the logistic family.
Suppose a certain retail store has customers whose ages are normally distributed such that μ=37.5 years and δ=7.6 years.(i) Calculate the probability that a randomly chosen customer is more than 48 years old. (ii) Calculate the probability that a randomly chosen customer is younger than 44 years old. (iii) Calculate the probability that a randomly chosen customer is between 46and 54 years old.
We assume that the car accident of a certain driver happen according to a Poisson N(t) of intensity lambda=0.01 per month. Compute the following (a) The probability that the driver has no accident during the first year (b) The probability of exactly one accident during his third year of driving. (c) the probability of at least two accidents before the end of the second year given that there was exactly one accident during the first year.
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
certain city, the daily consumption of water (in millions of liters) follows approximately a gamma distribution with rate = 0.5 and shape parameter=4. If the daily capacity of that city is 8 million liters of water, what is the probability that on any given day the water supply is more than the daily capacity? O 0.174 O 0.5665 O 0434 O 0.8264
Find the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1
The geometric distribution gives the probability that the first success occurs at the xth trial with success probability p. f(x)=(1-p)x-1p, x=1,2,3,... Show that E(X)=1/p
The Volatility X for the S&P stock index on a given day is a normal random variable with mean = 10 and standard deviation = 2 The volatilities recorded over a 100-day period on the S&P500 are Y1, Y2, ... Y100. Assume that these Yi's are independent and identically distributed, uniform on the interval [5,15]. Let V = (Y1 + Y2 + ... + Y100)/100. What approximately is P[9.5 < V < 10.5]?
If the number X of particles emitted during a 1-hour period from a radioactive source has a poisson distribution with parameter equal to 4 and that the probability that any emitted is recorded is p=0.9 find the probability distribution of the number Y of the particles recorded in a 1-hour and hence the probability that no particle is recorded
Suppose that a medical test has a 85% chance of detecting a disease if the person has it (P(PT|D)=0.85) and a 90% chance of correctly indicating that the disease is absent if the person really does not have the disease (P(NT|Dc=0.90). Suppose that 95% of the population does not have the disease P(Dc)=0.95 What is the probability that a randomly chosen person will test negative P(NT)?
Q3. Generate three random variates according to each of the following distributions using your own uniform random variates from U(0, 1) and list them: • Discrete Uniform: U (15, 17) • Uniform: U (0.57, 1.5). • Triangular: Triang (2, 10, 4). • Binomial: Bin (12, 0.4). • Lognormal: LN (5, 1). Beta: Beta (5, 5). • Negbin (8, 0.4) • Weibull (.5, 2.5) Geom (0.5) • PT5 (0.5, 0.5)

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