Let X be a random variable distributed as Normal(5,4). Find the probabilities of the following events: (i) P(X< 6). (ii) P(X> 4). (iii) P(|X – 5| > 1).

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A: Solution-: Let, X -be a continuously random variable takes values between 0 and c i.e. P( 0≤X≤c)=1…

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A: Note: Hey there! Thank you for the question. As you have posted multiple sub-parts, we have solved…

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Q: Let X and Y be independent normal random variables such that the mean and variance of X are 2 and 4,…

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Q: Let Y be the Exponential random variable withl > 0. Find the following probabilities. 1(1 3(1

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A: The density function is given by: f(x) =1/(50-40)        = 1/10

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A: Since , the probability function is given by ,  Our aim is to find the probability that X is odd.

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Q: A player will win if he rolls two dies and gets a sum equal to 6. If he plays 12 times, what is the…

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Q: Suppose that X is a Normal random variable with E(X) = 1 and Var (X) = 1. Define Y =2X + 1. Find P(0…

A: Consider, EY=E2X+1=2EX+1∵EaX+b=aEX+b=2*1+1=3 VarY=Var2X+1=22*VarX∵VaraX+b=a2*VarX=4*1=4 SDY=VarY=4=2

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A: The probability can't be exceed than 1 for any distribution.

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Q: Let X be a Poisson random variable with parameter 2. (i) What is the probability P(X > 1)? (ii) What…

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Q: If 'X' is a continuous random variable, then the expected value is given by

A: here use property of Continuous Random variable

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Q: Q1:Show that: If X1, X2, ,X, are independent random variables and X = X1 + X +...+ X, , then 02:…

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Q: Why is the probability that a continuous random variable equals a specific number zero?  That is,…

A: By definition,

Q: X has been defined as the Poisson random variable. Thus, P (X = 1) = 0.149 and P (X = 2) = 0.224 are…

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