The random variables X and Y have joint density function 2 f(x, y) = (x + 2y), 0 <æ < 1, 0 < y < 1. 3 Calculate the coefficient of correlation of X and Y. P(X, Y) = Are X and Y statistically independent random variables? Explain your answer briefly.

Q: Let X and Y be two continuous random variables with joint probability density 3x function given by:…

A: We know that, Var(X)= E(X^2)-(E(X))^2 so from the given values, = (3/5)-(3/4)^2 = 3/5 -9/16 =…

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Q: (d) Are the random variables X and Y independent? Justify your answer.

A: To check independence of X and Y we have to find marginal pdfs of X and Y.

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Q: 36. QUESTION: Let X have the density f(x) = 2x if 0 < r <1 and f(x) = 0 otherwise. Show that X has…

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Q: Sk(x + 4y) ,0 <x < 2, 0 < y < 1 ,otherwise Let f(x,y) = be the joint probability density of X and Y.

A: From the given information, f(x, y)=k(x+4y), 0&lt;x&lt;2, 0&lt;y&lt;1 The value of k is obtained…

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Q: The random variable X models the loss in thousands of dollars due to a fire in a commercial…

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Q: Let (X,Y) be bivariate random variables having joint probability density function as x) = ;(x + y)…

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Q: (iii) Find the marginal pdf's (iv) Find the joint cdf

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Q: A random variable has density function f(x)= = 1.6 1.2x, for 0 ≤ x ≤ 1. a) Calculate the variance of…

A: given function is f(x)=1.6−1.2x   for

Q: Let X and Y be two continuous random variables with joint probability density function: 8 xy ;0<…

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Q: * The waiting time T (in hours) between each SMS you receive is random with the density function.…

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Q: The(probability density function of a random variable, x is (x) = -(4 – x²) for 0< x < 2 4 = 0 %3D…

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Q: The wait T in hours between every phonecall a person recives is random given the densityfunction…

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Q: Q-6 The j.p.d.f of two continuous random variable, x and y are given by f(x,y)= x² + (xy/3), Osx<1,…

A: The formulas for Var(X), Var(Y), Cov(X,Y) and Corr(X,Y) are given as follows; Where E(Xr ) and E(Ys…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!