Exercise 3. Suppose S is the sample space formed by rolling 3 fair, 6-sided dice and recordingthe numbers seen: (81, 82, 83). Give the spaces (i.e. domains) of the following random variables:(a) X = S₁ + S2 + S3(b) Xmax(81, 82, 83) – min(81, 82, 83)(c) X = max(s₁, 82, 83) × min(81, 82, 83)(d) Run at least 30 trials, using real dice, google dice or a computer code (if you have experienceof computer coding), to estimate the relative frequencies (and therefore the pmf) of the r.v. frompart (b).=

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A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that we roll two fair dice, one red and one blue. Then there are 36 possible outcomes in the sample space, as shown in the table below. Blue Die 1 4 6. 1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 84 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) A 5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 6 (6,1) (6,2) (6,3) (6,4)| (6,5) (6,6) Suppose we write the sample space in terms of the number of dots facing up on the two dice. That is, write S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Use the table to answer each of the following: Complete the probability distribution function (pdf). Enter your answer as a fraction. Sample space Probability 2 3 4.
If A,B are two independent event in a sample space, if P(A) = 0.7,P(B) =0.6. Find P(AU B) Select one: a. 0.42 b. 0.82 c. 0,88 d. 0.28
4. In an organization consisting of 5 women and 10 men, a committee of four individuals is to be selected at random from the 15 people. Find the distribution of the random variable, X = Number of women on the committee. %3D
4.56 Nonstandard dice. Nonstandard dice can produce interesting distributions of outcomes. You have two balanced, six-sided dice. One is a standard die, with faces having one, two, three, four, five, and six spots. The other die has three faces with one spot and three faces with six spots. Find the probability distribution for the total number of spots Y on the up-faces when you roll these two dice.
1. Provide a Boolean Expression to simplify. This expression should involve an overbar over the entire expression. Present TWO different simplification proofs. The first: apply DeMorgan's law as the first step, the second: simplify under the bar first.
Suppose that three of your family (ex: mother,father and you) drop their cell phones at your house and that each of them picks up the cellphone at random, list the elements of the sample space S using using the letter O and N for own phone and not his/her own phone to be picked, respectively. To each sample point assign a value x of the random variable X representing the number of people who get their right cell phone . Complete the table below.
Assume that 900 births are randomly selected and 443 of the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
The sample space of an experiment is {A, B, C}. Find the probability of each outcome if P(A) = P(B) and P(C) = 2P(A)
Let A, B and C be events from a common sample space such that: P(A) = 0.72, P(B) = 0.56, P(C) =0.25, P(ANB) = 0.42. P(ANC) = 0.18, P(BOC) =0 %3D Compute P(AUBUC).
II. Supply the table with the corresponding random variable and/or the possible values of the random variable for each experiment. Possible values (x) for the Experiment Random Variable (X) Random Variable Number of customers who 1. Contacting 10 customers 0, 1, 2, 3, 4,5 placed a complaint 2. Inspection of shipment of 100 laptops 3. Filling a bottle of water (maximum of 500 mL) 0, 1,2, .,99, 100 0sxs 500 The temperature when the desired reaction takes place (minimum of 40°C; maximum of 90* C) 4. Testing of new chemical process 5. Selling an automobile O if male; 1 if female
A group of 100 BSSE girls from Riphah were selected to participate in a survey conducted by HEC to assess the satisfaction of students with online studies provided by the university. 48 % of the girls were high scorers while the rest were average scorers. 51 girls showed a lack of satisfaction with the studies including only 9 high scorers. Construct a 2 way cross tabulation and answer the following questions a. If a randomly selected student is an average score what is the probability that she would be satisfied with the studies b. What is the probability that a randomly picked student is a high scorer not satisfied with the studies c. What is the probability that a randomly picked students who is satisfied with the studies is a high-scorer girl

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Exercise 3. Suppose S is the sample space formed by rolling 3 fair, 6-sided dice and recordin the numbers seen: (81, 82, 83). Give the spaces (i.e. domains) of the following random variables: (a) X = S1 + S2 + S3 (b) X = max(81, 82, 83) — min(81, 82, 83) (c) X = max(s1, 82, 83) × min(81, 82, 83)