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Prolleo Y. We chooe a mmber from the ,2,3,...,100, miformly ai random. Let X be the...
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the...
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the order statistics o exponential distribution with mean β. Let (i) Are the random variables U,V,W independent? (ii) What is the distribution of each of U,V and W.
3. (a) A fair dice is tossed 6 times. Suppose A is the event that the...
3. (a) A fair dice is tossed 6 times. Suppose A is the event that the number of occurrences of an even digit equals the number of occurrences of an odd digit, while B is the event that at most three odd digits will occur i. Determine with reason if the events A and B are mutually exclusive. ii. Determine the probabilities of the events A and B. Are the events A and B independent? b) Suppose a fair coin...
A letter is chosen uniformly at random from {A, B, . . . , Z}. If...
A letter is chosen uniformly at random from {A, B, . . . , Z}. If that letter is one of the vowels (i.e. A, E, I, O or U) then a second letter is chosen uniformly at random from {A, B, . . . , Z}. Let L be the number of letters chosen and let V be the number of vowels chosen. (i) What is the expected value of L? (ii) What is the expected value of V?...
Let X and Y be independent exponential random variables with pdfs f(x) = λe-λx (x >...
Let X and Y be independent exponential random variables with pdfs f(x) = λe-λx (x > 0) and f(y) = µe-µy (y > 0) respectively. (i) Let Z = min(X, Y ). Find f(z), E(Z), and Var(Z). (ii) Let W = max(X, Y ). Find f(w) (it is not an exponential pdf). (iii) Find E(W) (there are two methods - one does not require further integration). (iv) Find Cov(Z,W). (v) Find Var(W).
LSM 3 Part A. Let X, Y be two exponential (2) random variables that are independent from each other. We know that X should have DF of x)for 20 and CDF of F)for20. 1. (5 credits) Let I-min(X, . Obt...
LSM 3 Part A. Let X, Y be two exponential (2) random variables that are independent from each other. We know that X should have DF of x)for 20 and CDF of F)for20. 1. (5 credits) Let I-min(X, . Obtain the PDE f) 2. (5 credits) Let 4 be the event (Xsy. Obtain the conditional joint PDE of (10 credits) Let IP-Y-X. Obtain the conditional PDF of fnIA (wIA) 3*.
LSM 3 Part A. Let X, Y be two exponential...
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2,...
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2, 3, 4, 5, 7 and 9 if digits may not be repeated? (ii) How many of the numbers so formed are even? (iii) How many of the numbers formed are divisible by 3? (iv) How many of the numbers formed are less than 700,000? (b) JACK MURPHY’s seven character password consists of four let- ters chosen from the ten letters in his name (all...
Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. (a) How many...
Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. (a) How many ways can this be done, if the order of the choices is not taken into consideration? x 6 ? (b) How many ways can this be done, if the order of the choices is taken into consideration? A teacher wanted to fairly choose three students from a class of 24 to raise the school's flag. He assigned each student a two-digit number from 01...
A box contains 5 green balls. We choose balls at random, with replacement, according to the...
A box contains 5 green balls. We choose balls at random, with replacement, according to the following rules: (i) Upon choosing each ball from the box, we mark it with a red stripe before replacing it in the box. (ii) We stop as soon as we choose a ball with a red stripe (i.e. the ball has been chosen twice). Let x= the number of times that balls were chosen from the box. (Note that x must be at least...
(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the...
(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the number left over after this repeated subtraction. The number Y is almost the same as the remainder left over after dividing N into X equal parts, ercept that Y will equal X, not 0, if N is evenly divisible...
Let X be a continuous random variable defined on R. Then for any real number x...
Let X be a continuous random variable defined on R. Then for any real number x True ● False The staff at a small company includes: 2 secretaries, 12 technicians, 4 engineers, 2 executives, and 64 factory workers If a person is selected at random, what is the probability that he or she is a factory worker? 21 16 21 19 21 7 A 7 digit code number is generated by randomly selecting digits, with replacement, from the set(1.23 the...
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the order statistics o exponential distribution with mean β. Let (i) Are the random variables U,V,W independent? (ii) What is the distribution of each of U,V and W.
3. (a) A fair dice is tossed 6 times. Suppose A is the event that the number of occurrences of an even digit equals the number of occurrences of an odd digit, while B is the event that at most three odd digits will occur i. Determine with reason if the events A and B are mutually exclusive. ii. Determine the probabilities of the events A and B. Are the events A and B independent? b) Suppose a fair coin...
LSM 3 Part A. Let X, Y be two exponential (2) random variables that are independent from each other. We know that X should have DF of x)for 20 and CDF of F)for20. 1. (5 credits) Let I-min(X, . Obtain the PDE f) 2. (5 credits) Let 4 be the event (Xsy. Obtain the conditional joint PDE of (10 credits) Let IP-Y-X. Obtain the conditional PDF of fnIA (wIA) 3*.
LSM 3 Part A. Let X, Y be two exponential...
Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. (a) How many ways can this be done, if the order of the choices is not taken into consideration? x 6 ? (b) How many ways can this be done, if the order of the choices is taken into consideration? A teacher wanted to fairly choose three students from a class of 24 to raise the school's flag. He assigned each student a two-digit number from 01...
(c) Let N~DU(100), and let X have the value 10, 20, 25, or 50 with probability 1/4 each, independent of N. If N > X, repeatedly subtract X from N until the result is X or smaller. Let Y be the number left over after this repeated subtraction. The number Y is almost the same as the remainder left over after dividing N into X equal parts, ercept that Y will equal X, not 0, if N is evenly divisible...
Let X be a continuous random variable defined on R. Then for any real number x True ● False The staff at a small company includes: 2 secretaries, 12 technicians, 4 engineers, 2 executives, and 64 factory workers If a person is selected at random, what is the probability that he or she is a factory worker? 21 16 21 19 21 7 A 7 digit code number is generated by randomly selecting digits, with replacement, from the set(1.23 the...
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