Let X be a continuous random variable with a probability density function f. Let the x-value a be such that P(X ≤ a) = 0.5. Let the x-value c be such that f(c) > f(x) for all x. = 10² Mean = bv b= x. f(x) dx Median = av Mode = CV Submit Question Q Search b

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Q: f(x) 0.5

A: It is an important part of statistics. It is widely used.

Q: Let X be a continuous random variable. Prove Var(X) > 0.

A: Solution:- Given that let X be a continuous random and prove that Var(X) > 0.

Q: Suppose that X and Y are independent random variables with the probability densities given below.…

A: Suppose that X and Y are independent random variables with the probability densities given below.…

Q: a) Probability function of X discrete random variable: P(- ) -{". x = 1, 2, 3, ...... 10 . ... in…

A: As you have posted multiple questions, we have provided answers for first question only as per our…

Q: Let X be a nonnegative continuous random variable with the pdf f(x). Read the following statements:…

A: Let X be non negative continuous random variable with pdf f(x).

Q: II. Let X be a discrete random variable with possible values xi, i=1,2,..., and p(xi)=P(X=xi) is…

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Q: d) If probability density functions of a random variable x is f(x) = {X² for-1≤x≤1 for any other…

A: f(x)=x2 ; -1≤x≤1

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Q: The life of a machine component has X days. The random variable X is defined by the P(X) P(X=x ) = {…

A: Note: " Since you have posted many sub-parts. we will solve the first three sub-parts for you. To…

Q: Prob. 4 (Gaussian Distribution) Consider a standard Gaussian random variable with probability…

A: INTRODUCTION :  Standard Normal Distribution:  fX(x)=12π e-x22    ; -∞&lt;x&lt;∞ calculation rules…

Q: Let X be a discrete random that takes values from the set {-2,0,2} where P(X=x)= { 1/5 if x=-2 3/5…

A: From the given information we want to graph graph of cumulative distribution function.

Q: a) Probability function of X discrete random variable: P(x) = { x = 1, 2, 3, .,10 in other cases (ex…

A: Hello! Thank you for the question, As per the honor code we are allowed to answer one question at a…

Q: 8. (a) Let f(x) be the pdf of a random variable X. if-2 ≤ x < 0 if 0 < x < 1 x² - 4x + 4 if 1 ≤ x ≤…

A: Farmula used P(X≤x)=F(x)

Q: 7) For the continuous probability distribution f(x) = kx³e-* Where x 20, find mean.

A:

Q: Let X be a random variable with the Chi-square probability density function. Derive the mean,…

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A: Here, need to give an example of a probability density function fX(x) whose associated continuous…

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Q: Q1. The density function of the random variable X is given by f(x) =% %3D 2. a) Verify that the…

A:

Q: a) Probability function of X discrete random variable: x = 1,2,3, ....,10 in other cases (CX P(x)…

A: Solution :  The PDF of random variable is given as, P (x) = cx                      x=1,2,3,...,10…

Q: Let X be a discrete ramdom Variable. whose probability distribution is defined as follows- p(X=x)=…

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Q: 4. Let X be a random variable whose probability density function is given by 3 0≤x≤2 3 2≤x≤2…

A: Ans#4- X be a random variable whose pdf is given by             f(x) = k,      0≤x≤32k2(2 - x),…

Q: Let the probability distribution of random variable X be P(X= k) k! , k = 0, 1, 2, I then EX2 - ()

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Q: find the value K and F(x).

A:

Q: Let X luck variable show μ = 1, σ2 = 1 parameter lognormal distribution. So what is the probability…

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Q: P(-∞ < x≤ a₁₂) = P(a₁ ≤ x ≤ a₂) = P(a₂ ≤ x ≤ a3) = P(a3 ≤ x < ∞) = function p(x) a₁ = = 1 π(1 + x²)…

A:

Q: Find Cumulative Distribution Function (cdf) of X, F(x), x {0, 1, 2,...}

A: The cumulative distribution function is: F(a)=∑x=0ac13x=c∑x=0a13x=c1301-13a1-13=c(1)1-13a23=3c21-13a…

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)…