Please see attached image... Let X be a continuous random variable with density functionx > 0f(x) = {3e-3x0,else.(a) Verify that f is a density function.(b) Calculate P(-1 < X < 1).(c) Calculate P(x < 5).(d) Caculate P(2 < X < 4|X<5)3

As per our guidelines we are suppose to answer only three sub parts . Given,f(x)={3e-3x; x>00;…

Let X be a continuous random variable with density function √ 3e-3x, 0, (a) Verify that f is a density function. (b) Calculate P(-1 < X < 1). (c) Calculate P(x < 5). (d) Caculate P(2 < X < 4|X<5) f(x) = x > 0 else.

Let X be a continuous random variable with density function √ 3e-3x, 0, (a) Verify that f is a density function. (b) Calculate P(-1 < X < 1). (c) Calculate P(x < 5). (d) Caculate P(2 < X < 4|X<5) f(x) = x > 0 else.

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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Question

Please see attached image...

Let X be a continuous random variable with density function
x > 0
f(x) = {
3e-3x
0,
else.
(a) Verify that f is a density function.
(b) Calculate P(-1 < X < 1).
(c) Calculate P(x < 5).
(d) Caculate P(2 < X < 4|X<5)
3

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