6.43. Let X and Y be, respectively, the smallest and the largest values of two uniformly distributed values on (0,1). Find the conditional density function of Y given X € (0,1). Also, show that X and Y are not independent. = x,
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- A student has 3 volumes of short stories and 2 novels on a bookshelf. She selects 3 books at random to take home over vacation. A random variable X is defined to be the number of novels selected. Find the values assumed by X and its density function.2. Let X and Y have the joint density given by: f(x, y) = k(2x+y) for 0 < x, y < 1 0 otherwise where k is a constant. Find k. Also, obtain the conditional density, conditional mean and conditional variance of Y given X = ½ (14 pointelThe time T a business is closed after a fire has the cumulative distribution function (부)- 3 1 1 F7(t) = t>0 t+1 otherwise = VT. The cost to the insurer is X = Determine the density of X for x > 0.
- 7. Assume that X and Y have joint probability density function given by (2x + 3y) if 0< x<1 and 0Let X and Y random variables have independent Gamma distributions with X-Gamma(1, 6) and Y-Gamma(2, B). a. Find the joint probability density of Z, = X + Y, Z, = X+Y a. Find the marginal pdf of Z2.Let X have the uniform distribution on the interval [1, 3]. Find the density function of Y =X^2.endent. 3.60 The joint probability density function of the ran- dom variables X, Y, and Z is ry=", 0 }, 2 < Z < 3); (d) P(0 < Z < 2 | X = , Y = }). 75°F Mostly cloudy24. Consider a distribution with density on the interval [0, 2]. Let the probability density function (pdf) for this distribution be the following: fy(u) = % on [0, 2] 2 (i) Draw/plot the pdf fy(y) vs. y for the interval [0, 2]. (ii) Determine the Cumulative Distribution Function (CDF), F, (y). (iii) Draw/plot the CDF F,(y) vs y for the interval [0, 2]. (iv) Determine the expected value of the Random Variable (RV) y, i.e., E [y].Suppose that X and Y have a joint probability density function given by ce-3z=5y if a, y 20 fx.y(T, y) = otherwise Find the marginal probability density function fx and state the name of the distribution of X.Q9) Find the correlation of the * following joint density function f(x,y) 1 2 0.5 0.2 1 0.3 -0.25 O -0.212 -0.08909 -0.32733 O -0.35635 O 2.Please provide Handwritten answerhp.com/h20195/v2/GetDocu- Q4. The probability density function of the RV X is f(x) = 5e-kx for x 20. Find 2) bslubsribe ni Ilia ( a) the value of k. b) the probability that x>1. 1.19 ani PHICS c) If Y~N(2,2). X and Y are independent, then find the P(0.25 ≤X ≤ 0.5 and 0.1 ≤Y ≤ 0). sri 200 sulev 19 vode antiw baworla) 126 9di vino b 200 rasl Bus 5 minim ert zienW SHX 1211 65 290100 to af Ye 910255m of b990 neupentSEE MORE QUESTIONS
