3. A discrete random variable X has a cumulative distribution function (edf) defined by0.00 if r<10.30 if 1< r < 30.40 if 3 12F (x) =(a) Calculate the probability P(3 1.2)(b) Find the value of the mean for the continuous random variable X.

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Answered: 3. A discrete random variable X has a…

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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Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s). (f) Calculate P(M = 30) using a normal approximation with the continuity correction.
Let Y be a binomial random variable with n = 10 and p = 0.3. (a) P(3 < Y < 5) = P(3 ≤ Y < 5) = (b) P(3 < Y ≤ 5) = P(3 ≤ Y ≤ 5) =
Suppose a random variable X is best described by a uniform probability distribution with range 0 to 6. Find the value of a that makes the following probability statements true. (a) P(X a) = 0.79 a = (d) Р(X > а) — 0.13 a = (e) P(2.61 < X < a) = 0.03 %3D
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
A continuous random variable X has cumulative distribution function F(x) = 1.5 3 2 6 –1 < x < 1. a) Find the expected value of X using the definition of expectation.
Suppose X is a discrete random variable which only takes on positive integer values. For the cumulative distribution function associated to X the following values are known: F(23) 0.34 F(29) = =0.38 F(34) 0.42 F(39) 0.47 F(44) = 0.52 F(49) 0.55 F(56) = 0.61 = Determine Pr[29
My Find the standard deviation of the discret probability dist x P(x) xp(x)) (x-M)² | (x-mipul 2 σ = √(x-M)² pxx) ટે О 0.21 10*0.21=0 /10-112 =. M= Exp(x) 1 0.30 1*0.3 = 0.3 2 0=49 EXP(X) =M

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3. A discrete random variable X has a cumulative distribution function (cdf) defined by 0.00 if r<1 0.30 if 1 4) (c) Compute the probability mass function (pmf) of X by completing the following table for f (x). 1 6 12 f(#) the avnoatad Y G. find F(Y))