Let a random experiment be the cast of a pair of unbiased dice each having six faces, anc let r.v. Y denote the sum of the dice. Sketch the p.d.f. g(y) of Y. Find P(Y <1)
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- b) The table below shows a random sample of respondents consists of 109 local and 91foreign visitors and the island they preferred to vacation. Island Respondent Redang Island (R) Tioman Island (T) Rawa Island (W) Pangkor Island (P) Local (L) 34 2a a 15 Foreigner (F) 5/2 b 38 18 b i) Find the value of a and b .ii) Find the probability, P(T' U F).○ Let assume 6 balls, 3 white, 2 black and 1 red. Random experiment is selection of three balls with replacement. R.v. X denoted number of white balls and r.v. Y denotes number of red balls. O P(X=2, Y-2)= 0 O Probability of which events is zero? O P(X=1, Y=2) = Compute joint pmf of X and YSecond Rubber Balls in a Box Setup Stars Stripes Dots 12 Red 8. 15 Blue 7 3 14 Green 2 9. 6. Experiment: The rubber balls all have the same size, texture, weight, etc. They ca distinguished without looking at them. The rubber balls are mixed around thorou the box. One rubber ball is to be drawn randomly. Let X = the color on the rub Let Y = the pattern on the rubber ball. 23. Use the Second Rubber Balls in a Box Setup. Find P( X = Green OR Y = Stars ). 57 А. 76 59 В. 76 61 С. 76 63 D. 76
- 6- The Variance of X, is a) o? b) d) 25.3 A bent coin, with heads probability .2, is tossed 13 times. Let X be the number of heads in the 13 tosses. Find (a) P(X =5), and (b) P(X = 12).Consider the experiment of rolling 3 fair four-sided dice (the numbers on each die are 1,2,3 and 4). X 1, X 2 and X 3 denote the numbers on the first, second, and third die, respectively. Y = X 1+X_2+X_3, the sum of the three rolls. What is E(X_2]Y)? 3.5 O 2.5 OY/2 Y/3 Ox2 X_2
- 2.Direction: Classify the random variables as DISCRETE OR CONTINUOUS. 1. ev 3. 4. The 5. The speed of a car. 6. M 7. eigit of Elfel To 8. 9Percentage of the population of Kalinga. 10 Frequency of radio station. 2. ed ner houcebel Afa period Dallaing a piect. dronit in rs. touns Paris.point) Four buses carrying 157 high school students arrive to Montreal. The buses carry, respectively, 33, 50, 25, and 49 students. One of the studetns is randomly selected. Let X denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on his bus. Compute the expectations and variances of X and Y: E(X) = Var(X) = E(Y) = Var(Y) =Second Rubber Balls in a Box Setup Stars Stripes Dots Red 8 15 12 Blue 7 3 14 Green 9. 6 Experiment: The rubber balls all have the same size, texture, weight, etc. They cannot be distinguished without looking at them. The rubber balls are mixed around thoroughly in the box. One rubber ball is to be drawn randomly. Let X = the color on the rubber ball. Let Y = the pattern on the rubber ball. 16. Use the Second Rubber Balls in a Box Setup. Find P( NOT Y = Stripes NOT X = Green ). 39 A. 59 45 D. 59 41 В. 59 C. 43 С. 59 *** MORE PROBLEMS ON THE NEXT PAGE. ***