Suppose that X is a random variable whose density function is defined as follows: (a+1) æª fx(x) = 2a+1 with 0 -1. For a = 1.15 calculate the IQR of X.

Q: 2kx/45' 0 < x < 5 f (x) = 2k(30 – x)/45 5 < x < 10 0, otherwise

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A: The  is a continuous random variable. The PDF is, Here, The objective is to find .

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Q: Let the random variable X follow a gamma distribution with α = 4 and β = 4. If Y = X2 what is the…

A: Given, X~ Gammaα=4,β=4 Y=X2

Q: 3. Let A be a parameter. Show that the family of functions fa(x) = x >0 is a probability density…

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Q: Suppose that the random variable B has the standard normal density. What is the conditional…

A: Step 1: The two roots of the equation x2 + 2Bx + 1 = 0 are real only if  |B| ≥ 1.  Since P(|B| ≥ 1)…

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Q: |If the expected value of the random variable X is 1/3. Find the values A and B.

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Q: Q21. Consider a linear amplifier defined by input-output relation Y = ax +b where a and b are…

A: ANSWER: For the given data,

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A: From the given information, a1,.....,an are iid samples from a distribution with density…

Q: Let X have the pdf f(x) = B¬l exp{-x/ß}, 0< x<o∞o. Find the moment generating function, the mean,…

A: The moment generating function is defined as MX(t) = E(etx)

Q: Suppose that Y Еxponential() ~ and let X = exp{-Y/ß} be a new continuous random variable. If…

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Q: Suppose that the random variable X has density function fx (x) = bxb-1 for 0 < x < 1, where b is a…

A: The median of a probability density function, f(x) is calculated using the formula,               ;…

Q: f (x) Suppose a continuous random variable X has the probability density K (1-x²) for 0 < x < 1, and…

A: It is give that  a continuous random  variable X has the probability  density function f(×) =…

Q: i) Derive the standard error of B, se (B) = 0.0009, using MLE approach. ii) Find an approximate 95%…

A: Firstly it is required to determine the MLE of the parameter and then the variance to get the…

Q: The random variable X has probability density function 1 < x < 2 f(x) = otherwise. Calculate Var(4X…

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Q: have a coin loaded such that P(heads) = 3/7 and P(tails) = 4/7. suppose that the coin is tossed…

A: Given that, I have a coin loaded such that P(heads) = 3/7 and P(tails) = 4/7. suppose that the coin…

Q: Let the random variable Y possess a uniform distribution on the interval (0,1). Use the…

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Q: Suppose that X1,.…,X, is a random sample from a distribution with density f(x; 0) = 0x-?, r E (8,…

A: We have given that Let X1 X2 ....Xn be the random sample of size n having the probability density…

Q: ) Write the joint probability density function. p) Express F(z) = P(¥ <z) using integrals and…

A: Let X and Y be continuous independent random variable have exponential distribution with mean θ

Q: a) Let X₁, X2, X3,..., X30 be a random sample of size 30 from a population distributed with the…

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Q: Let X ~ U(a,b). Use the definition of the mean of a continuous random variable to show that μX =…

A: The mean of the uniform continuous random variable can be calculated as:

Q: Let x be a random variable with probability density function, f(x) = C (1- x^2), -1 < x < 1  and ‘0’…

A: a. The probability density function of the random variable x is given by, f(x) =…

Q: i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95%…

A: Firstly it is required to determine the MLE of the parameter and then the variance to get the…

Q: Suppose that X is a random variable with the probability density function given by (2(1-x), 0≤x≤1…

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Q: Let X₁, X2, X3,..., X30 be a random sample of size 30 from a population distributed with the…

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Q: Let X be a continuous random variable with PDFfx(x)= 8/x3, x> 2. Find E[W where W = X/3.

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Q: Suppose that X1, X2, . . . , X7 are i.i.d. random variables, each with density function f(x)=…

A: In question, We have given X1, X2, . . . , X7 are i.i.d random variables having pdf f(x). And M is…

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A: From the given information, U1 and U2 are independent and each has an exponential distribution with…

Q: Let T be a continuous random variable having the following probability density function: et – 1…

A: Given information: The probability density function of the continuous random variable is as given…

Q: Let X₁, X2, ..., Xn be a random sample from a population with probability density function 4 ƒ(2) =…

A: The probability density function (PDF) of the random variable  is given as,The random sample  of…

Q: Exercise 2: Show that .0965 is the joint probability density for two independent random variables X₁…

A: dnorm() is a R function that is used to calculate the probability density of a normally distributed…

Q: For a statistic to be a good estimator of a parameter, two properties it must satisfy are…

A: It is given that Xi~Expθ; i=1,2,3 with  EXi=θ, EX2i=2θ2, and VarXi=θ2. The sample mean of  X is…

Q: Suppose Yı and Y2 are random variables with joint pdf fr,x,V1.Y2) = { o. S6(1 – y2), 0 < y1 < y2…

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Q: 4. The lifetime in hours of an electronic gadget is a random variable having a probability density…

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