If the probability density of a random variable is given by 0 < X < 1 otherwise ĮK (1 -- X2) fx (x) = Find: (i) K (ii) the distribution function of the random variable.

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Q: 4.

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A: Solution: From the given information, the probability density function of X is

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Q: 2. Suppose that a continuous random variable X has PDF f(x) = }7 (1 – x²) -1<x<1 else

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A: Basic formula for variance and expectation are used in the given solution

Q: 1. If the probability density of the random variable is given by 630x (1- x) for 0<x<1 flx) =…

A: Given: The distribution given is as follows fx=630 ×x4×1-x4             0&lt;x&lt;1

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A: ANSWER: For the given data,

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A: f(x)=(k+2)x3        0&lt;x&lt;10                           o/wproperities∫f(x)dx=1

Q: If the probability density of a random variable is given by JK (1 X2), 0< X < 1 0 < X< 1 fx (x) =…

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Q: The diameter of a bolt (in mm) is a random variable with probability density function: [6(x – 12)(13…

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Q: A continuous random variable X has the distribution function F(x) = 0 if x 3 The value of k is

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Q: 1.1. Suppose random variable X is distributed as normal with mean 2 and standard deviation 3 and…

A: As per bartleby guidelines we can solve only first question and rest can be reposted