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- Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X) c.) Find Var(X) d.) Find E(3 *squareroot(X))If the joint probability is given by:f(x,y) = (3x + 2y)/40, for x = 0, 1, 2, 3; y = 0, 1, 2, 3 a.) Find P(X>Y ): b.) Find P(X > 2, Y ≤ 1): c.) Is the equation valid? YES OR NO d.) Find P(X ≤ 2, Y = 1): e.) Find P(X + Y = 4):The common probability function of X and Y random variableslike thisa. Find the value of Cov (X, Y).b. U random variable defined as U = X + YFind the probability function.
- X and Y are independent, X ~ U (0, 1) and Y U (0, 1). Calculate the probability P(X+Y<1.5).b) Let Z₁-N(0,1), and W₁ = Y~N(0,1), for i=1,2,3,...,10, then: dx dy i) State, with parameter(s), the probability distribution of the statistic, T = - 154 ii) Find the mean and variance of the statistic T = ₁² 10 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of ß such that P(T> B) = 0.01, where T = ₁2₁² +².Let X~N(2,1), Y~N(-1,2). X and Y are independent. Find the probability distribution for Z=X - 2Y.
- Use a Venn diagram. Let P(Z) = 0.44, P(Y) = 0.28, and P(Z U Y) = 0.57. Find each probability. (a) P (Z'n Y') (b) P(Z'U Y) (c) P (Z' U Y) (d) P (Zn Y')b) Let Z₁ = X-X~N(0,1), and W₁ i) State, with parameter(s), the probability distribution of the statistic, T = ox YHY~N(0,1), for i=1,2,3,...,10, then: oy 10 ii) Find the mean and variance of the statistic T = ² 1,²₁² Σt=12₁ SiaWi iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of ß such that P(T> B) = 0.01, where T = Σ₁Z₁²+₁Wi².For the continuous probability function f (x) = Kx² e* when x20 fint i) k i) mean iii) variance