Q3: A continuous random variable T has the following probability density function: f(t) = (3(1-t/k) -{3(1 Find the following: A) k. B) E(T). C) Var (T). Ost≤k, t> k

Q: Let X be a continuous random variable with the following pdf: (3x²+1), f(x) = { ¼ (3² -1<a<1…

A: Let X be a continuous random variable with the following pdf:

Q: I. Let X be the number of courses that thirty part-time students were taking this term. The…

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Q: fx(x) = {{ √ x/2 01 Let Y be the output of the "clipper": Find: a) The probability P[Y = 0.5] b) The…

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Q: Say we have a continuous random variable X. Let f(x) = c(1 + x²) for support S = [0,1] and c being a…

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Q: Q.5 The probability density function for a continuous random variable T is 0≤x≤ 8, fr (t) = {au; 8…

A: For fT​(t) to be a valid pdf, its integral must equal 1. ∫−∞+∞​fT​(t)=∫08​at dt+∫89​8a…

Q: A18 Let (Y₁,..., YK) be multinomially distributed with parameters n and p₁,...,PK. Let Y₁,..., YK E…

A: 18) We have given information regarding the multinomial distribution. Then we have to find the…

Q: Let f(x) be the probability function of the geo(p) distribution. Prove that: a) f(x) is indeed a…

A: Given that fx be the probability function of the geop distribution.

Q: A manufacturer guarantees a product for 1 year. The lifespan of the product after it is sold is…

A: Given: f(t) = 0.008e-0.11t  if t ≥ 0

Q: Let the random variable X have the pdf f(x) = 2(1-x), 0 < x < 1 and zero elsewhere. ( round your…

A: Given that the pdf of random variable X is   f(x)=2*(1-x)                         ,0&lt;x&lt;10…

Q: 4. Suppose the joint PDF of two random variables X and Y are given below. |(ry² + x²y), if 0 < 1< 1,…

A: The joint pdf of two random variable x and y is given: fX,Yx,y = cxy2 + x2y,if 0≤x≤1, 0≤y≤1…

Q: What is the expectation (to 2 decimal places) of Y? ELY

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Q: Let the joint pdf of random variables X, Y be fx,y (r, y) = axye-2-3y, for all æ > 0, y 2 0. Find a,…

A: We have given that a joint pdf of variables X and Y.

Q: Y is an exponential random variable with parameter 1 = 0.2. Given the event A = {Y < 2}, a. What is…

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Q: where 0 0. Let Y =- log X. Find the distribution of Y. . Let X1,..., X, be independent and…

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Q: Q2 Let (X₁, X₂) be jointly continuous with joint probability density function 2e (²1+2₂) 0 f(x1, x₂)…

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Q: (8) A continuous random variable T has p.d.f. defined as t f(t) = C. (2+1)² for t > 0 anf f(t) = 0…

A: Pdf is f(t)=ct1+t2; t&gt;0