The probability distribution function for normal distribution is given by _(x-µ)² e 202 o V2n f(x) = where x is a continuous random variable. If o = 3, µ = 5 and 2< x < 8, find P(2 < x < 8) using (i) Newton Cotes integration formula with n = 6,

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A:

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A: Given  mean=3 np=3..(1) standard deviation=√2 variance=2 np(1-p)=2 3(1-p)=2 From the equation (1)…

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A: We have given that, Let X be a random variable with pdf,   f(x) = (1/2)e-|x|       -∞&lt;x&lt;∞.…

Q: x~e^. ofY=3x+2 and Z= X/4 Find the distratoution

A: Solution

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A: Given p.m.f. is  f(x)=13                    x=-1,0,1     =0                        otherwise

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A: The time X is takes to reboot a certain system has gamma distribution with E(X)=3 min and Var(X)…

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Q: If X ~B(60,0.18), use the normal distribution to approximate the binomial distribution for: (i)…

A: Given, X ~B(60,0.18) i.e., n=60 p=0.18 P(X=10)=?

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A: Given: PX=k=e-a×akk!    k=0,1,2.............α=E(x-μ3)σ3ϕ(s)=Eesk

Q: Q2/ Let X be a random variable with normal distribution N(0,4) and Y=(X+2)² find:- 1- P(Y > 1) 2-…

A: Given Information: Let X be a random variable such that X~Nμ=0,σ2=4 and Y=X+22.

Q: A portfolio has an expected rate of return of 0.15 and a standard deviation of 0.15. The risk-free…

A: Risk tolerance refers to the amount of risk an investor is willing to take achieve an investment…

Q: Q4: The strength of the cubic concrete of the first line production is 110 N/mm and standard…

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Q: X is a normally distributed variable with mean μ = 35 and standard deviation σ = 5. Find a) P(x 21)…

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A: Given that it needs 5meters of stick to make a picture frame.

Q: A random variable X has a distribution function given by; f(x)={kx; 0<or=x<or=1, k(4-x^2);…

A:

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Q: (1) Find the distribution of V=X₁ - X₂.

A: E(X1-X2)=E(X1)-E(X2)=μ-μ=0

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A: The region in which f=b is shown in figure:  f=0 for other values of (m,n)

Q: The heights (x) of students are normally distributed with mean 152 cm and standard deviation 30 cm,…

A: normal distribution μ = 152 cmσ = 30 cmP(x&lt;140) = ?

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Q: If X ∼ Gamma(2, 5), find E(X^2 ) andE(X^4 )

A: Solution: Let X follows gamma distribution with the parameters 2 and 5.

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Q: T has an exponential distribution such that P(TS2)=2P(T>4) What is Var(T)=

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Q: The heights (x) of students are normally distributed with mean 154 cm and standard deviation 34 cm,…

A: normal distribution μ = 154 cmσ = 34 cmP(x&lt;136) = ?

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A: Wr have given that F(x) = ( x + A)/8 , x = 1,2,3 Where range of x is Rx = {1,2,3}

Q: solve using normal distribution rules x ~ n (25,5^2) find k such that p(20

A: Mean()=25Standard deviation()=5

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A: Probability function  f(x) = c2xe-cx       x≥0

Q: You have two random variables M and N where the joint pdf is given by  f_M,N(m,n) = 1/2 if m + n…

A: