1.8. Expectation of a Random Variable 67 1.8.8. A bowl contains 10 chips, of which 8...
5. A bowl contains 7 chips, which cannot be distinguished by a sense of touch alone. Three of the chips are marked $1 each, two are marked $3 each and the last 2 are marked $5 each. A player is blindfolded and draws, at random and without replacement, two chips from the bowl. The player is paid an amount equal to the sum of the values of the two chips that he draws and the game is over. a) What...
A box contains 5 chips marked 1,2,3,4, and 5. One chip is drawn at random, the number on it is noted, and the chip is replaced. The process is repeated with another chip. Let X1,X2, and X3 the outcomes of the three draws which can be viewed as a random sample of size 3 from a uniform distribution on integers. a [10 points] What is population from which these random samples are drawn? Find the mean (µ) and variance of...
Let a bowl contain 10 chips of the same size and shape. One and only one of those chips is res. Continue to draw chips from the bowl, one at the time and at random without replacemeent, until the red chip is drawn. Let x be the number of trials needed to draw a red chip. a) Find the probability mass function of x. b) Compute Pr[x
10 point A box contains three defective and seven non defective chips. Three chips are drawn randomly without replacement one after the other. Let X be the # of defective chips. Using hyper geometric model construct the probability distribution of X and show that it fulfills the two conditions of probability distribution. Also find E(X) 1 Add file Page 2 Back Submit LALAR
3. (10 points) Let X be continuous random variable with probability density function: fx(x) = 7x2 for 1<<2 Compute the expectation and variance of X 4. (10 points) Let X be a discrete random variable uniformly distributed on the integers 1.... , n and Y on the integers 1,...,m. Where 0 < n S m are integers. Assume X and Y are independent. Compute the probability X-Y. Compute E[x-Y.
8. Let X1...., X, be i.i.d. ~E(1) random variables (i.e., they are independent and identically distributed, all with the exponential distribution of parameter 1 = 1). a) Compute the cdf of Yn = min(X1,...,xn). b) How do P({Y, St}) and P({X1 <t}) compare when n is large and t is such that t<? c) Compute the odf of Zn = max(X1...., X.). d) How do P({Zn2 t}) and P({X1 2 t}) compare when n is large and t is such...
5. Five bowls are labeled 1 - 5. Bowl j contains j white and 5-j red balls. Example: Bowl 2 contains 2 white and 3 red balls. One bowl is selected at random and two balls are selected (without replacement). (a) What is the probability both balls are white? (b) What is the probability both balls are red? (c) What is the probability one ball is red and one ball is white? (d) Write out the probability distribution for the...
10. Let Y1,..., Y, be a random sample from a distribution with pdf 0<y< elsewhere f(x) = { $(0 –» a) Find E(Y). b) Find the method of moments estimator for 8. c) Let X be an estimator of 8. Is it an unbiased estimator? Find the mean square error of X. Show work
1. In a box there are three numbered tickets. The numbers are 0, 1 and 2. You have to select (blindfolded) two tickets one after the other, without replacement. Define the random variable X as the number on the first ticket and the random variable Y as the sum of the numbers on your selected two tickets. E.g. if you selected first the 2 and second time the 1 , then X = 2 and Y-1 +2 = 3. a./...
1. (6 pts) Consider a non-negative, discrete random variable X with codomain {0, 1, 2, 3, 4, 5, 6} and the following incomplete cumulative distribution function (c.d.f.): 0 0.1 1 0.2 2 ? 3 0.2 4 0.5 5 0.7 6 ? F(x) (a) Find the two missing values in the above table. (b) Let Y = (X2 + X)/2 be a new random variable defined in terms of X. Is Y a discrete or continuous random variable? Provide the probability...