Pleaase solve Let ? denote the amount of time a randomly selected student needs to finish this test and suppose thatthe cdf of ? is given by:Refer screenshotEstimatea. ?(? ≤ 1)b. ?(0.5 ≤ ? ≤ 1)c. The pdf of ?, ?(?)d. The expected value and the variance of ? 3. Let X denote the amount of time a randomly selected student needs to finish this test and suppose thatthe cdf of X is given by:0,x < 0;F(x) =0 2.EstimateP(X < 1)P(0.5 < X < 1)The pdf of X, f(x)The expected value and the variance of Xа.b.с.d.

Name: Pleaase solve Let ? denote the amount of time a randomly selected stud
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Description: Pleaase solve Let ? denote the amount of time a randomly selected student needs to finish this test and suppose thatthe cdf of ? is given by:Refer screenshotEstimatea. ?(? ≤ 1)b. ?(0.5 ≤ ? ≤ 1)c. The pdf of ?, ?(?)d. The expected value and the varian

a) The probability is calculated as, PX≤1=F1=124=14=0.25 b) Solve for the probability as,…

Answered: 3. Let X denote the amount of time 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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Pleaase solve

Let ? denote the amount of time a randomly selected student needs to finish this test and suppose that
the cdf of ? is given by:

Refer screenshot

Estimate
a. ?(? ≤ 1)
b. ?(0.5 ≤ ? ≤ 1)
c. The pdf of ?, ?(?)
d. The expected value and the variance of ?

3. Let X denote the amount of time a randomly selected student needs to finish this test and suppose that
the cdf of X is given by:
0,
x < 0;
F(x) =
0<x< 2;
x > 2.
Estimate
P(X < 1)
P(0.5 < X < 1)
The pdf of X, f(x)
The expected value and the variance of X
а.
b.
с.
d.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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3. Let X denote the amount of time a randomly selected student needs to finish this test and suppose th the cdf of X is given by: 0, x² 0 2. Estimate P(X < 1) P(0.5 < X < 1) The pdf of X, f(x) The expected value and the variance of X а. b. с. d.