x is a uniform random variable in the interval (x1,x2). Find the expected value of x
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x is a uniform random variable in the interval (x1,x2). Find the
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- Let X and Y be any two random variables and let a and b be any two real numbers. Then var(ax + bY) = a² var(X) + b?var(Y) + 2ab cov(X,Y). False TrueLet P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).Let X and Y be two independent random variables distributed uniformly on the interval [0, 1]. What is the probability of the event Y ≥ given that Y≥1-2r?
- A kindergarten class consists of 12 boys and 4 girls. The children are arranged from tallest to shortest. Assume that all 16! rankings are equally likely, and no two children are the exactly the same height. let the random variable X be the rank of the second tallest boy. assume that the tallest person in the class is rank 1. (a) find f(x) (b) Calculate E[X] and V[X]Let X and Y be independent random variables with the distributions X ∼ Geometric(p = 1/3)and Y ∼ Geometric(p = 2/3). Find Pr[X = Y].Let random variable X be the number of users communicating with a cellular base station within a given time interval. Its PMF is :
- Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.If is a random variable that has a uniform distribution on the interval [0, 10], then p(x+ 27) PX+ is equal toExercise 3. Let X be a random variable with mean and variance o². For a € R, consider the expectation E((X-a)²). a) Write E((X-a)²) in terms of a, u and o². b) For which value a is E((X - a)²) minimal? c) For the value a from part (b), what is E((X-a)²)?
- Let X be a random variable and c be a constant. Then Var(X+c) = Var(X), always. True FalseFor each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete. (d) X = the length of a randomly selected rattlesnake Describe the set of possible values for the variable. 0, 1, 2, 3, ... 1, 2, 3, ... [0, ∞) (0, ∞) State whether the variable is discrete. discrete not discrete (e) Z = the sales tax percentage for a randomly selected amazon.com purchase, where n = the total number of possible sales tax percentages for online purchases Describe the set of possible values for the variable. z1, z2, z3, ..., zn [0, zn] 1, 2, 3, ..., n [0, n] State whether the variable is discrete. discrete not discrete (f) Y = the pH of a randomly chosen soil sample Describe the set of possible values for the variable. 0, 1, 2, 3, ..., 14 [0, 14] 1, 2, 3, ..., 14 (0, 14] State whether the variable is discrete. discrete not discrete (g) X = the tension (psi) at which a randomly selected…Choose points from (0, 1) uniformly and add the numbers together. Stop this process when your add is greater than one. Let N be the random variable which is the number of points that you selected. Find E(N).