8. The probability density function is f(x) = k(3x² - 1) -1≤x≤2 =0 otherwise Find (i) the value of k, and (ii) P(-1 ≤ x ≤ 0).

Q: 2) Let the joint probability function of X & Y be defined by Pxx (x, y) = x= 1,2 y = 1,2,3 Find…

A: The joint probability mass function of x and y is, P(x,y)=x+y21;x=1,2 and y=1,2,3 x=1, y=1…

Q: x (10-x) Q1. Show that f(x): ;0<x < 10; is a probability density function. 5000

A: To be a probability density function, the sum of all f(x) must be 1. so we must…

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Q: =) Find u and o.

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Q: The distribution function ‘F’ is given by F(x) = 0, x < 0 ½, 0 ≤ x <1 3/5, 1 ≤ x < 2 4/5, 2 ≤ x < 3…

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Q: variable is given by P(X = r) = kr³,r = Q.#2 (a) If the probability mass function of a random 1,2,3,…

A: a) (i)To find the value of k, use the condition of valid pmf…

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Q: Suppose Y ~ Uniform(01,02) where the parameters 01 and 02 take the values -4 and -3 respectively.…

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Q: (b) Let X be a continuous random variable with probability density function p(x) -Ca+e on (0,2). i.…

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Q: For the probability distribution, find d. P(y = 6) e. f(y = 4) f. f(y= 6) g. F(y = 5.5) h. F(4) f.…

A: Since total probability is always 1:P(Y=−2)+P(Y=−1)+P(Y=0)+P(Y=1)+P(Y=2)=1

Q: (E,-0,) Estimate 0 by minimizing the function where E, is the expected number of j=1 losses in the…

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Q: x (10-x) Q1. Show that f (x) = ;0<x< 10; is a probability density function. 5000

A: To prove that f(x) is a probability density function, we need to show that f(x) adds up to 1.…

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Q: f(x), a continuous probability function, is equal to 1/20 , and the function is restricted to 3 ≤ x…

A: Given,f(x)=120    ;   3≤x≤23

Q: (E,-0,) Estimate 0 by minimizing the function where E, is the expected number of j=1 losses in the…

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Q: If the continuous random variable X has the probability density ( 62(1 - 2) for 0<z<1 elsewhere f(2)…

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Q: Let X and Y be two independent continuous random variables whose joint probability distribution is…

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Q: b) For the triangular function c(10-x) 0<x<10 f(x)={° otherwise Find the value of c which makes the…

A: From the provided information,

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Q: Let X1 ~ Exp(1) and X2 ~ Exp(^2) be independent exponential random variables. (a) When A1 2,…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: X is a discrete variable with the probability distribution B(18, 0.35) Determine the value of Fx(4).

A: given data : binomial distribution  X~B(18,0.35) n = 18 p = 0.35 FX(4) = ?

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Q: f(x) for a continuous probability function is 1/18 , and the function is restricted to 2 ≤ x ≤ 20.…

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Q: a. Verify that f(y) = 1 b. What is the probability that total waiting time is at most 8 minutes? ∞

A: Here given probability density function of total waiting time for two buses .

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

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Q: Let A = {3, 4, 5}, and B = {−5, -3, -2, -1}. Define a relation R from A to B as follows: For all (x,…

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Q: Q5. The probability density function for a random variable X is given by Jax + bx², 0≤x≤1 otherwise.…

A: The probability density fraction for a random variable X is given by:The objective is to find

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Q: f(x), a continuous probability function, is equal to 1/12, and the function is restricted to 0<x<12.…

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Q: Find the probability that in Family of y children will least (1) boy - probability male birth is…

A: Solution : Probability of at least one boy = 1- probability of 0 boys. probability of 0 boys =…

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Q: The score of a student on a certain exam is going to be a number between 0 and 1. Think of it as the…

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Q: Suppose one randomly chooses a values X on the interval (0, 2), and then random choosing a second…

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Q: Find (i) P (X 0.3 ?

A: