Question

Applied and Computational Questions 1. Pairs of random numbers (r, y) a. How many different pairs are possible? are generated. X and Y are integers between 0 and 5 inclusive. a random variable W is defined to equal the absolute value of the difference between X b. Suppose and Y. How many distinct values are possible for W? Give the pair of dice is rolled once. 2. Let x represent the number of times a one appears when a probability distribution for x. 3. A small bag of M&M candies has the following assortment: red (10), blue (2), orange (5), brown (21), green (0), and yellow (18). Let x count the number of candies of each oolor, give the probability distribution for x 4. Find all values of k so that the following is a probability distribution: 1 2 3 4 P(@) 0.15 2k 0.52 k 5. Find the mean and standard deviation of the following probability distribution: 1 3 2 P(E) 0.3 0.2 0.5 =10.25. Find the 6. A probability distribution has a standard deviation equal to 2.5 and r2P(z) mean for this distribution. 7. An arsenal contains several identical boxes of ammunition, If the number of defective bullets per box has the following distribution, find the mean and standard deviation for x. 2 P(z) 0.90 0.07 0.03 8. Calculate the standard deviations of the following two probability distributions, both of which have a mean equal to 5. Distribution A: 6 4 5 0.8 0.1 0.1 P(r) Distribution B 8 6 7 2 3 4 1 0.1 0.2 0.05 P(r) 0.05 0.2 0.1 0.05 0.2 0.05

Answer 1

(Page No. Date: Solution 1 3 Henc HaIS O S2 2k ue kenaw fhet o.15+2kt052 k=1 3KELICA67 3k 33 Heng gich 0:5 E) x) =sCo 3 )f2@S)+3(0. 2 F(X)J9 O.3t1 OS -103)+4(05)f9a 2) EG)-A 1O 3+2+I E)=41 N(x)=E(x2)-DECA) N()= 0 19 4-C) CQPS 2P)- 10 25 =ECX) Her gich, sd) 2 vx)E()-EC)] 2 10.25-6 25 2