A value=2 A -2 It is known that for a random variable X, the Expectation of...
Let X be an exponential random variable with parameter 1 = 2, and let Y be the random variable defined by Y = 8ex. Compute the distribution function, probability density function, expectation, and variance of Y
#5 please
2. Find the probability distribution function for the random variable representing picking a random real number between -1 and 1. (This is a piecewise defined function.) 3. Compute the mean of the random variable with density function if x>0 ed f(r) = if r < 0. 0 4. Compute the mean of the random variable with density function 2e (1 - cos x) if x >0 if r<O. f (x) = 5 Compute the variance and standard deviation...
O RANDOM VARIABLES AND DISTRIBUTIONS Expectation and variance of a random variable Let X be a random variable with the following probability distribution: Value x of X P(X-) 0.35 0.40 0.10 0.15 10 0 10 20 Find the expectation E (X) and variance Var(X) of X. (If necessary, consult a list of formulas.) Var(x) -
Consider a continuous random variable X with the following
probability density function:
Problem 2 (15 minutes) Consider a continuous random variable X with the following probability density function: f(x) = {& Otherwise ?' 10 otherwise? a. Is /(x) a well defined probability density function? b. What is the mathematical expectation of U (2) = x (the mean of X, )? c. What is the mathematical expectation of U(z) = (1 - 2 (the variance of X, oº)?
Q1. [4 marks Find the expectation and standard deviation of the uniform random variable X that takes values 2, 4, 6, 8, .,98. Hint: consider the random variable Y X/2.
Q1. [4 marks Find the expectation and standard deviation of the uniform random variable X that takes values 2, 4, 6, 8, .,98. Hint: consider the random variable Y X/2.
Problem 2. Assume that random variable X has normal distribution with mean 2 and standard deviation of 5 (1) Find the density of random variable Y = X3. (2) Find the mean and variance of random variable Y defined above in (1)
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
(6) Suppose that X is an absolutely continuous random variable with density 1<I<2 f(3) = lo, otherwise. Find (a) the moment generating function MX(t). (b) the skewness of X (c) the kurtosis of X (7) Suppose that X, Y and Z are random variables such that p(X,Y) = 1 and p(Y,Z) = -1. What is p(X, Z)? Explain your answer. (8) Suppose that X, Y and Z are random variables such that p(X,Y) = -1 and p(Y,Z) = 0. What...
Find the variance of random variable X. 7.. Let X be a continuous random variable whose probability density function is: -(2x3 + ar', if x E (0:1) if x (0;1) Find 1) the coefficient a; 2) P(O.5eX<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given X 8 -2 0 2 8
3 The probability density function of a random variable on the interval [9, 16] is f(x) = x. Find the following values. a. Find the expected value The expected value is (Round to two decimal places as needed.) b. Find the variance. The variance is (Round to two decimal places as needed.) c. Find the standard deviation The standard deviation is (Round to two decimal places as needed.) d. Find the probability that the random variable has a value greater...