10) The X random variable has a normal distribution. P(X > 15) = 0.0082 and P(X<5)...
2. If X and Y are independent random variables, X has a normal distribution with mean 2 variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find u such that P(X > 2+11,7)=0.01.
A. Random variable X has a binomial distribution, B(36, 0,5). Use the normal approximation, Compute P[15Kx<19)- B. Random variable X has a normal distribution, N(50, 100) Compute P(X < 41 or X>62.0)
4.) a.) Suppose that X is a normal random variable with mean 4. If P[X > 9} = 0.1 approximately what is Var(X)? (15 points) b.) Measure the number of kilometers traveled by a given car before its transmission ceases to function. Suppose that this distribution is governed by the exponential distribution with mean 800,000. What is the probability that a car's transmission will fail during its first 40,000 kilometers of operation? (10 points)
Suppose that X is a random variable that has a normal distribution with mean u= 5 and standard deviation o = 10. Evaluate the following probabilities: (a) Pr(X > 10) (b) Pr(X < 2) (c) Pr(6 < X < 11) (d) Pr((X – 10)2 < 12)
Let X be a discrete random variable that follows a Poisson distribution with = 5. What is P(X< 4X > 2) ? Round your answer to at least 3 decimal places. Number
5. Suppose X is a discrete random variable that has a geometric distribution with p= 1. a. Compute P(X > 6). [5] b. Use Markov's Inequality to estimate P(X> 6). [5] c. Use Chebyshev's Inequality to estimate P(X>6). [5] t> 0 6. Let be the probability density function of the continuous 0 t< 0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that...
6. Let X be a normal random variable with mean u = 10. What is the standard deviation o if it is known that p (IX – 101 <>) =
A random variable, x, has a normal distribution with u = 11.6 and 6 = 2.50. Determine a value, Xo, so that a. P(x>xo) = 0.05. b. P(xsxo) = 0.975. c. P(H-Xo xxx H +0) = 0.95. a. Xo = (Round to one decimal place as needed.) b. Xo (Round to one decimal place as needed.) C. XO (Round to one decimal place as needed.)
9. The distribution function of a random variable X is given by 0, for r<-1, F(x) = { 271 -1<x<1, 1, 2 > 1. Find (a) P(Z < X < }); (b) P(1<x< 2).
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]