6. For a continuous probablity distribution, 0 s xs 15. What is P(x > 15)?
For the continuous distribution below, what does the shaded area represent? P(x > 0) P(6 < x < 7) P(x>7) P(0 < x < 6)
(15 points) Let X be a continuous random variable with cumulative distribution function F(x) = 0, r <α Inr, a< x <b 1, b< (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
P(x=a) 1 Note that for a discrete random variable, 0 Therefore P(xS a)? P(x<a) A.= C. 7 D. 2
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).
< 0) = 1/3, and Exercise 9.8. Suppose X has an N(u,02) distribution, P(X P(X < 1) = 2/3. What are the values of u and o?!
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a Inz, a<<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function S(x) for X. (d) Find E(X)
number? 10 3. Let X be a continuous random variable with a standard normal distribution. a. Verify that P(-2 < X < 2) > 0.75. b. Compute E(지)· 110]
Homework: Week #6( sec. 6.1,6.2, 6.4) | 11 of 20 (8 complete) > Score: 0 of 1 pt 6.4.29 A random variable follows the continuous uniform distribution between 20 and 50. a. Calculate the following probabilities below for the distribution. 1. P(x 35) 2. P(x 530) 3. P(x540) 4. P(x=32) b. What are the mean and standard deviation of this distribution? a. 1. P(x 5 35) = (Type an integer or decimal rounded to three decimal places as needed.) Enter...
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
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1