Find the value of a when Z is a standard normal random variable and P{-3 < Z <-1} = P{1 < Z

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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Q.2 Find the value of x when Z is a standard normal random variable and P{-3 < Z <-1} =
P{1 < Z <x}.
2.37
O
CHE ar
Transcribed Image Text:Q.2 Find the value of x when Z is a standard normal random variable and P{-3 < Z <-1} = P{1 < Z <x}. 2.37 O CHE ar
Expert Solution
Step 1

What is Cumulative Distribution Function:

The cumulative distribution function (CDF) of a real-valued random variable X assessed at x in probability theory and statistics is the likelihood that X will have a value less than or equal to x. It provides the area under the probability density function from minus infinity to x in the case of a scalar continuous distribution. The distribution of multivariate random variables is also specified using cumulative distribution functions.

Given:

For a random variable Z following standard normal distribution, it is given that, 

P-3<Z<-1=P1<Z<x

To Determine:

We determine x.

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