10. Suppose that a random variable X has the uniform distribution on the interval [-2,8). Find...
5. A continuous random variable X follows a uniform distribution over the interval [0, 8]. (a) Find P(X> 3). (b) Instead of following a uniform distribution, suppose that X assumes values in the interval [0, 8) according to the probability density function pictured to the right. What is h the value of h? Find P(x > 3). HINT: The area of a triangle is base x height. 2 0 0
Suppose that U is a random variable with a uniform distribution on (0,1). Now suppose that f is the PDF of some continuous random variable of interest, that F is the corresponding CDF, and assume that F is invertible (so that the function F-1 exists and gives a unique value). Show that the random variable X = F-1(U) has PDF f(x)—that is, that X has the desired PDF. Hint: use results on transformations of random variables. This cute result allows...
lo (P15) Suppose X is a random variable with the uniform distribution over the interval (1.2) and Y = X4 (a) Compute P[Y St] as a function of t. You need to distinguish three different cases. (b) Find the probability density function of Y and use it to compute EY).
18. suppose that the random variable X has a continuous uniform distribution over [ 10, 20 ]. Find P (15 is less than or equal to X is less than or equal to 19 ) Possible answers : A 0.30, B 0.35, C 0.40, D 0.45
Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. Refer to Exhibit 6-1. The probability density function has what value Select one: O a in the interval between 20 and 28? 1.000 O b. C. 0.125 d. 0.050 Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over ase interval from 20 to 28 Refer to Exhibit 6-1. The probability that x will take on...
2. Assume that the pdf of the random variable x is uniform in the interval (10, 12) and y = x^3. (a) Find fy (y). (b) Find E{y}.
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.
A random variable, X, has uniform distribution on the interval [0,θ] where θ is unknown. A hypothesis test is as follows: H0: θ = 2 H1: θ ≠ 2 It has been decided to reject H0 if the observed value of x is x ≤ 0.1 or x ≥ 1.9. Part a: Find the probability of committing a Type I error. Part b: Suppose the true value of θ is 3. Find the probability of committing a Type II error....
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).
Suppose that the random variable X has the discrete uniform distribution f(x) = { 1/4, r= 5, 6, 7, 8. 0, otherwise. A random sample of n = 45 is selected from this distribution. Find the probability that the sample mean is greater than 6.7. Round your answer to two decimal places (e.g. 98.76). P= the absolute tolerance is +/-0.01