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GATE CS 2022 : Engineering Mathematics -6
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Question 1
Consider the following probability density function with continous random variable.
f(x)=100e-100x, if x
0
= 0, if x<0
Find the probability that x is greater than 0.01.
f(x)=100e-100x, if x
0 = 0, if x<0
Find the probability that x is greater than 0.01.
Question 2
Consider a company having a database of their customers over 10 years and the number of malfunctions of product reports over 5 year has a poisson distribution with λ=2. The probability that there is at least one malfunctioning report is
Question 3
Let X be a random variable with probability density function
f(x)=x+1, if -1<x<0
=1-x, if 0
x<1
= 0, otherwise
If E(X) is expectation of X, find E(X2). (Round upto two decimal places)
f(x)=x+1, if -1<x<0
=1-x, if 0
x<1 = 0, otherwise
If E(X) is expectation of X, find E(X2). (Round upto two decimal places)
Question 4
The cumulative distribution function of a random variable x is the probability that X takes the value
Question 5
Determine the probability distribution function corresponding to the below density function.
, where 
Question 6
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?
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