3. Given the cumulative distribution function of a continuous variable X,0,x < 0-fireAx², 0

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Answered: 3. Given the cumulative distribution…

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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If the prob density of a rv is given by f(x)=kx² 0
13.THEORY OF DISTRIBUTIONS
8. The probability density function is f(x)=k(3x² - 1) -1≤x≤2 =0 otherwise Find (i) the value of k, and (ii) P(-1 ≤ x ≤ 0). r
6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, o0) is a function f such that f(r) 20 and (2) = = 1. (a) Determine which of the following functions are probability density functions on the (-x0, 00). fr-1 00 (b) We can also use probability density functions to find the erpected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. rf(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.
A random variable X has a probability density function 0; x<0, f(x) = 0≤x≤ 1, ; 1
Q2. The probability density function of X is as follows. f(x) = 2 - 2x, for x = [0, 1] Which one of the following expressions can be used to find P(0.5 < X < 1.5)? F(x) is the cumulative distribution function of X. (A) 1 - F(0.5) (C) F (1.5)-f(0.5) (B) f(1.5)-f(0.5) (D) 1.5 (2 - 2x) dx (E) other
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1. Suppose that for a certain life the probability density function is x (*) 1+x ,x >0 X. Find (i) the survival function ofx (ii) the probability that the life aged 25 will die within next 15 years. (iii) the probability that the life aged 42 will die between 55 and 62.
15. A random variable X has probability density function 2x, 0 0.75 /X > 0.5).
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3. Given the cumulative distribution function of a continuous variable X, x < 0 0