Let X be a continuous random variable whose probability density function is: x ≥ 1 0, x < 1 Then compute the following probability (Type your answers in decimals) f(x) = 21
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- Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?Suppose that two-dimensional continuous random variable (X, Y) has joint probability density function given by f(x,y) = 24xy, x is less than equal to 1 and greater than equal to 0, y is less than equal to 1 and greater than equal to 0, x+y is less than equal to 1 and greater than equal to 0. Check that E(Y) = E[E(Y|X)] and V(Y) = E[V(Y|X)] + V[E(Y|X)].Let continous random variable x taking on values over the set [0,a] and has a probability density function fx(x) = C exp(-nx), x = [0,a] where a = 1.1, n = 2.3. Find C
- Suppose that X is a continuous random variable with density function f(x). If f(x)=k for −5≤x≤3 and f(x)=0 otherwise, determine the value of k.Let the random variable Y denote the time (in minutes) for which a customer is waiting for the beginning of a service station since its arrival and let X denote the time (minutes) until the service is completed since its arrival at the service station. Since both X and Y measure the time since the arrival of the customer at the service station, always Y<X is true. The joint probability density function for X and Y is given as follows: fxy(x,y)=c(x+y) for 0<x<2 and 0<y<x what is the value of c? what is the covariance of X and Y? what is the correlation of X and Y?Let X be a continuous random variable with density functionf(x) = 3x^-4, x ≥ 1. Compute E(X ) and Var(X ).
- Determine the conditional probability distribution of Y given that X = 1. Where the jointprobability density function is given by f(x,y)=1/64xy for 0 < x < 4 and 0 < y < 4.A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0The probability density function of the continuous random variable X defined in the set of non-negative real numbers is given as f(x) = 2.exp(-2x). What is the expected value of X?
- On a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?Let X and Y be two continuous random variables with joint probability density function f(x,y) = 2xy for 0 < x < y < 1. Find the covariance between X and Y.Let x be a random variable defined by density function fx=3x^2 define less than equal to 1 and great than equal to 0 and 0 is defined by otherwise. 1) find E(X) 2) Find E(X^2)