
![(d) p (1x-1012c) < 0.04 - 30.04 ac =100 =) C= 10 [ (in posidive] - Thumbs up.]](http://img.homeworklib.com/questions/69af1bd0-1f1c-11ea-bac6-f1f366341ce8.png?x-oss-process=image/resize,w_560)
8. A random variable X has a mean u = 10 and a variance o= 4. Using Chebyshev's theorem, find (a) P(X – 10 > 3); (b)...
A random variable X has a mean μ = 10 and a variance σ2-4. Using Chebyshev's theorem, find (a) P(X-101-3); (b) P(X-101 < 3); (c) P(5<X<15) (d) the value of the constant c such that P(X 100.04
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 <>) =
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).
10) The X random variable has a normal distribution. P(X > 15) = 0.0082 and P(X<5) = 0.6554 find the mean and variance of this distribution
Let X ~ Geomeric(p). Using Chebyshev's inequality find an upper bound for P(|X – E[X]] >b).
2 of 3 01- 5. Suppose X is a discrete random variable that has a geometric distribution with p= 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)
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
5. Let X > 0 be a random variable with EX = 10 and EX2 = 140. a. Find an upper bound on P(X > 14) involving EX using Markov's inequality. b. Modify the proof of Markov's inequality to find an upper bound on P(X > 14) in- volving EX? c. Compare the results in (a) and (b) above to what you find from Chebyshev's inequality.
Find the variance of random variable X. 7.. Let X be a continuous random variable whose probability density function is: -(2x3 + ar', if x E (0:1) if x (0;1) Find 1) the coefficient a; 2) P(O.5eX<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given X 8 -2 0 2 8
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)