The probability density function of a continuous random variable is: 4 (1+x) if -1 < x < 0 x < 0) 5 f(x) = 4 3 if 0 ≤ x <= < 15 Derive the distribution function of ! (Solution: (3 - 2x) 0, if xse1

Q: True or False;  For a continuous random variable X, P(X=x) = f(x) 1. True 2.False

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A: For the p.d.f to be valid, ∫1∞kx-2dx=1⇒k∫1∞x-2dx=1⇒k-1x1∞=1⇒k-1∞+11=1⇒k(0+1)=1⇒k=1

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A: here given cumulative probability density function

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

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Q: X is a continuous random variable having p.d.f. f(x) such that f(x) = kx2 Osxs5 otherwise Find : (a)…

A: According to our guidelines we can supported to answer only first three subparts   Given

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A: f(x)=2x ; 0&lt; x&lt; 1 n be the sample size

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Q: The probability mass function of a random variable X is given by 1 X f(x) = P(X = x) F(x) = P(X ≤ x)…

A: You have posted multipart  questions , we are allowed to solve only first three parts. Please post…

Q: 2/7, The cumulative distribution function of the discrete random variable X is F(x) = - 6/7 1 (A) 1…

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A: the random variable X has probability density function f(x) given by;f(x)=1x-12≤x≤e+10otherwise

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Q: The random variable x follows a uniform probability distribution in the interval (0,1); the…

A: We know that  The pdf of Uniform distribution is  f(x) = { 1/(b-a) ,   a&lt;x&lt;b                0.…

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Q: Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5]  a.) Find k b.) Find E(X)…

A: GIVEN DATA : X is the random variable with probability density function fx=k10-2x in the interval of…

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Q: Q2/(a) Let X be a random variable with p.d.f. kx 1<x<∞ S(x)= { find k. o.w (b) Let Xbe a random…

A: The p.d.f of X is valid if and only if ∫1∞fxdx=1⇒∫1∞kx-2dx=1⇒k∫1∞x-2dx=1⇒k…

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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: The probability distribution f the discrete random variable X is f(X) for x = 0, 1, 256 2, 3, Fin}E…

A: Given: fx=3x41x433-x256      for x=0,1,2,3

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Q: random variable X has a PDF f(x)=C(8*x−x^2) for 0<x<8, and is equal to 0 outside this range. (a)…

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Q: The time, in 100 hours, that a student uses her game console over a year is a random variable X with…

A: Step 1:Step 2:Step 3:Step 4:Final Answer (a). 77.667(b). 1492.955

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Q: If the random Variable x has a uniform distribution the interval [0,5] on Find P(2<XS4).

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Q: Q1 (a) A fair coin is tossed 5 times and the random variable X counts the number of heads that come…

A: Expected values are obtained.

Q: Let the probability function of the random variable X be f(x) = {  x/45 if x = 1, 2, 3, ⋯ ⋯ ,9…

A: