X is a uniform random variable on the integers from 3 to 6.
Find V(X).
solution:

Answer: V(X) = 0.75
[ Note: short cut formulas - Mean = E[X] = a+b/2 , variance = (a-b)^2 / 12 ]
X is a uniform random variable on the integers from 3 to 6. Find V(X).
The probability density function for a random variable X with a discrete uniform distribution over the integers 1, 2, 3, 4, 5, and 6 is f(x) = 1/6 for x = 1, 2, 3, 4, 5, 6. What is the mean of the distribution of X? The probability density function for a random variable X with a discrete uniform distribution over the integers 1, 2, 3, 4, 5, and 6 is f(x) = 1/6 for x = 1, 2, 3, 4, 5,...
Let the random variable X have a discrete uniform distribution on the integers 10 x 20, Determine the mean, μ, and variance, σ', of X Round your answers to two decimal places (e.g. 98.76) 14.85 3.12
Let X and Y be independent random variables. Random variable X has a discrete uniform distribution over the set {1, 3} and Y has a discrete uniform distribution over the set {1, 2, 3}. Let V = X + Y and W = X − Y . (a) Find the PMFs for V and W. (b) Find mV and (c) Find E[V |W >0].
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.
Let X be a uniform(0, 1) random variable and let Y be uniform(1,2) with X and Y being independent. Let U = X/Y and V = X. (a) Find the joint distribution of U and V . (b) Find the marginal distributions of U.
Let X be a random variable from a uniform distribution over [0,3]. Find the expected value of
Let X be a random variable following a continuous uniform distribution from 0 to 10. Find the conditional probability P(X >3 X < 5.5). Chebyshev's theorem states that the probability that a random variable X has a value at most 3 standard deviations away from the mean is at least 8/9. Given that the probability distribution of X is normally distributed with mean ji and variance o”, find the exact value of P(u – 30 < X < u +30).
a) If X is a discrete uniform random variable ranging from 1 to 10.find the expected value of at least 8? b) at any events, is p(A I B ) = p( B I A )
6: Suppose the random variable X has the uniform distribution on [a,b]. Find expression involving a and b for the expected value, variance, and standard deviation of X. Check that you expressions when a = 0 and b = 10 agree with what you got in part c) of problem 5.
Let the random variable X have a uniform distribution on [0,1] and the random variable Y (independent of X) have a uniform distribution on [0,2]. Find P[XY<1].