.Let X be a random variable with the gamma probability density function. Derive the MSE of T=X² +2X

Q: Find the variance of a random variable X with the given probability density function: f(x) = 3x2 for…

A:

Q: Consider the following probability density function of a random variable 360x"(1 – x)2 ,0 0.26) b)…

A: Given:fx=360x71-x2=360x71+x2-2x=360x7+x9-2x8=360x7+360x9-720x8                       ;0≤x≤1

Q: If the probability density function of a continuous random variable X is 0.50x 01.5)

A:

Q: If x is a random variable with a probability density function defined by the form x20 , S(x) =…

A:

Q: Let X be a Gaussian random variable with zero mean and variance equal to 2. 1-Find the probability…

A: It is given that, X be a Gaussian random variable with zero mean and variance equal to 2. That is,…

Q: If the probability density function of the random variable X is S1- |a| for |æ| < 1 f (x) = { 0, el…

A: The equation to find out the variance of a continuous random variable , when the PDF is given is ,…

Q: Verify that p(x) = 6x-1 is a probability density function on [1, ∞) and calculate its mean value.…

A: We are providing you the solution of last question which belongs to "Probability and Statistics",…

Q: Let x be a random variable with a probability density function defined by the form f(x) = ke */2, x…

A: We have given that X be a random variable with a probability density function defined by the form…

Q: Given is the following probability density function f(x) = e*; x > 0 The expected value of y=e3/4x…

A: Probability Density Function: A continuous function f(x) is said to be the probability density…

Q: Assume that the range of X is [4.9, 5.1] mA, and assume that the probability density function of X…

A: given; probability density function of X is f(x)=5   for 4.9≤x≤5.1 Variance=?

Q: . If X is an exponential random variable with parameter B = 1, find the probability density function…

A:

Q: Suppose that X is a continuous random variable whose probability density function is given by (C(4x…

A:

Q: Consider a continuous random variable with the following probability density function: f(x) = 4 x°,…

A:

Q: Let X be a random variable with probability density function given by x -1 0 1 f(x) a b 0.25

A: From the given information, x -1 0 1 f(x) a b 0.25 From the probability condition,…

Q: Find the mean and standard deviation of the specified probability density function. 1 f(x) = for…

A: Given that, the function is fx=18 and the interval is 12,20. Obtain the mean a+b2.…

Q: If a random variable X has the probability density function Sxe-* ,x > 0 ,otherwise' f(x) = Then…

A: Given,   fx = xe-x      ; x&gt;00             ; otherwise

Q: 1ine the probabilities that (d) x is less than 2.2 (e) between 1.4 and 1.6 (f) Calculate mean and…

A:

Q: Assume that the range of X is [4.9, 5.11 mA, and assume that the probability density function of X…

A: Solution

Q: Consider the probability density function for a random variable X, given by for 0 < x < 5 10 f(x) =…

A:

Q: Consider the probability density function for a random variable X, given by for 0 < x < 5 10 f(x) =D…

A: For the given random variable X, its probability density function is given by

Q: Consider the probability density function x, for 0 < x < 1 f(x) = {2 - x, for 1 < x <2 0, %3D…

A:

Q: 1. The random variable Y = X2 does not have a normal distribution because the probability density…

A: Given that,  X~ N(u,σ2)  Where u is mean and σ2 is variance of X.  P.d.f. of X is given by,    Y= X2

Q: If the probability density function of the random variable X is: -X e X>0, f(x) = 0, Otherwise. Then…

A: Here we need to find the Mgf of the given density function. It is clear that the above density…

Q: Consider the following probability density function for a random variable X. 2 1sx54 S(x) =9 10…

A:

Q: Consider the probability density function f(x) = 2x if 0 <x<1 %3D The Expected Value E(x) 2/3 .a O…

A:

Q: 7. The probability density function of a random variable X is f =;sin x in 0 SXST = 0 elsewhere ,…

A: The probability density function is fx=12sinx    , 0≤x≤π

Q: Suppose that the random variable X has the probability density function c(1 – x²) for - 1s x s1 f(x)…

A:

Q: Suppose that X is a continuous random variable whose probability density function is given by (4x –…

A: Given:

Q: Consider the following probability density function 0 < x < 2 (æ) = { +(4 – x) 2<x < 4 %3D |…

A:

Q: The probability density function of Y = 5X + 3 is:

A: To obtain the probability density function of Y=5X+3, we will use the transformation method.

Q: Let the random variables X and Y have the joint probability density function 3 fx,y(x, y) = 0 < x <…

A:

Q: Suppose that the random variable X has the probability density function c(1– x?) for - 1< x <1 f(x)…

A: Answer - The random variable X has  the probability density function                f(X) = c(1-x2)…

Q: Suppose that the random variables X and Y have the following joint probability density function.…

A: Solution

Q: For what value of c is the function {3 [c/x5 if x 2 1 f(x) otherwise a probability density function?

A: Obtain the value of C. The value of C is obtained as follows; Probability Density function:

Q: If X ~ U(3, 15), what is the probability density function for this distribution?

A:

Q: If p(x) is a probability density function such that; The first moment EX = 0.3 and the second moment…

A: Provided information is, First moment is E(X) = 0.3 and second moment is E(X2)=2.8 Variance is…

Q: (a) Find the mean and the variance of the random variable X, where f(x) is the probability density…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.

A:

Q: Suppose that X is a random variable with probability density function given by: fx (x) = { k(x³ +…

A: To find k k∫02(x3+x) =1kx44+x2202 =1k164+42 =1k=16

Q: Suppose that random variable X is uniformly distributed between 5 and 25. Draw a graph of the…

A:

Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: Given: ƒ(x) = kx3; [2, 4] A probability density function equals 1 for sum of all range of values.

Q: Consider a random variable X with probability density function f (x) given by 0.2 f(x) = { 0.2x –…

A: The given density function is:

Q: If X is a uniform random variable in (-2 , 4) and Y = X² – 4, the probability density function g(y)…

A:

Q: Consider two independent random variables, S and T, which are both exponentially distributed with…

A: Given:  Random variables  S and T  are independent and  follow exponential distribution (λ) With mgf…

Q: Let X be a random variable with the following probability density function: f (x) = (1 – a2), –1 < x…

A: According to Bartleby policy I have solved first three subpart of this question. I hope it will help…

Q: Determine the probability density function of the random variable X* if x 1 ON|30

A:

Q: Consider a continuous random variable with the following probability density function: f(x) = 4x', 0…

A: We have given that,  X be a continuous random variable having probability density function is,  f(x)…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!