3-1.1 Two random variables have a joint probability distribution function defined by F(x, y) = 0 x < 0, y < 0 = xy 0≤x≤1,0≤ y ≤1 = 1 x > ly > 1 a) Sketch this distribution function. b) Find the joint probability density function and sketch it. c) Find the joint probability of the event X < and > .

Q: A discrete random variable X has a Geometric distribution with E(X) = 1.5. Calculate P(X > 5). %3D

A: It is given that the mean is 1.5.

Q: Part d, e, f

A: Given that  Probability mass function of X is  x 0 1 2 3 4 f(x)= P(X=x) 0.3 0.1 ? 0.2 0.3…

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Q: please solve explain both part a and b for my understanding

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A:

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A: The probability mass function for the X can be defined as:

Q: B) Suppose two dice are tossed. Let X be the sum of the dots on the top faces of the two dice. Find…

A: The problem can be solved using the concept of expectation and PMF.

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A: HERE GIVEN PROBABILITY FUNCTION SO HERE CUMULATIVE PROBABILITY = F(a) = P  (X&lt;a)

Q: triangular probability density I, if 0<x <1, f(x) = 2 – x, if 1<x < 2, 0, otherwise. Part a) Find…

A: The distribution function of X wen it lies between 0 and 1 will be:

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: Define the random variable Z = U + V. a) Determine the joint probability mass function pu,z (u, z) =…

A: Given that U and V are independent r.v.s following geometric distn with pmf

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Q: Find the value of a

A: A function  f: ℝ→ 0,1 is said to be a probability density function if i.  f(x)≥0 and ii. ∫-∞∞f(x)…

Q: Suppose a discrete random v mass function (where c> 0 is a constant): 1 5c p(w) 2c

A: According to the sum, a) We know, ∑w=04p(w)=1 So, 2c+5c/4+c/2+c/4=1 Or,4c=1 Or, c=1/4 The value os…