Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval...
Consider the continuous random variable X, which has a uniform distribution over the interval from 0.46 to 0.96, what is the probability that X will take on a value between 0.62 and 0.84?
1. The continuous random variable X, has a uniform distribution over the interval from 23 to 43. a) What in the probability density function in the interval between 23 to 43? 6. 7: Total : _ 16 14 /25 b) What is the probability that X is between 26 and 33? c) What is the mean of X? 2. Given that z is a standard normal random variable, a) what is the probability of z being greater than-1.53? b) if...
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
Central limit theorem 9. Suppose that a random variable X has a continuous uniform distribution fx(3) = (1/2,4 <r <6 o elsewhere (a) Find the distribution of the sample mean of a random sample of size n = 40. (b) Calculate the probability that the sample mean is larger than 5.5.
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
2. Assume the random variable y has the continuous uniform distribution defined on the interval a to b, that is, f(y) = 1/6 - a), a sy<b. For this problem let a = 0 and b = 2. (a) Find P(Y < 1). (Hint: Use a picture.) (b) Find u and o2 for the distribution.
Let x be a continuous random variable with a uniform distribution. x can take on values between x=20 and x=54. Compute the probability, P(26<x<39). P(26<x<39)= ? (Give at least 3 decimal places) Let x be a continuous random variable with a uniform distribution. x can take on values between x=13 and x=52. Compute the probability, P(27<x<36). P(27<x<36)= ? (Give at least 3 decimal places)
Consider a random variable which has a uniform probability density on the interval (0.11. That is. p(x)-1 for 0ex Which of the following expressions is the variance of ? Choose 2 of the following answers. □ 1/2 xp(x)dr 1112 1/8 □ 114 □ 1/24
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).
Suppose that X is a continuous random variable with probability distribution Suppose that X is a continuous random variable with probability distribution O<x<6 18 (a) Find the probability distribution of the random variable Y-10X 3. fr o) 2 Edit for Sy s (b) Find the expected value of Y