Example 2:The following table gives the probability distribution of a discrete random variable X:X01234567P(X)0.11 0.08 0.240.140.180.170.020.06Find the following probabilities:1. P (X= 3)4. P (2< X < 6)2. P (X<2)5. P (4< X < 7)7. Probability that X assumes at most 38. Probability that X assumes at least 53. P (X> 4)6. P (1 < X < 5)

Given: The probability distribution of a discrete random variable X is given below: X P(X) 0…

Answered: Example 2: The following table gives…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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a. Which of the following CANNOT be a probability distribution? Explain.i. p(x) = x / 6 for x = 1,2,3ii. p x = x for x = 1,2,3iii. p(x) = x / 5 for x = 1,0,1 b. An investor has $1000 available for a 1-year investment. The investor isconsidering the following three options:Option APossible return 30% 20% 0% -20%Probability 25% 40% 20% 15%Option BPossible return 50% 30% 0% -40%Probability 15% 50% 20% 15%Option CGuaranteed return 10%Probability 100%i. Based on the expected returns, which of these options should theinvestor choose?ii. Compute the standard deviations for Option A and Option B. Whichone of options A, B, and C has the least risk (i.e. the smallest standarddeviation), which one has the highest risk? What can you say aboutthe relationship between the expected returns and the risks of financialassets in the normal situation?
The following table contains the probability distribution for X = the number of re-transmissions necessary to successfully transmit a 5 GB data package through a double satellite media. X P(x) 0 0.40 1 0.30 2 0.25 3 0.05 Find the probability that there is at most two re-transmission. The probabilities that discipline officers will discover violations of the student handbook in a certain school in a quarter are given in the following table. Number of Violations (v) 3 4 5 6 7 8 9 Probability P(v) 0.3100 0.1200 0.1700 0.1200 0.1300 0.1000 0.0500 What is the probability that on a given day, discipline officers will discover at most 6 violations of the student handbook? (Input answer in 4 decimal places) type your answer...
Consider the following discrete probability distribution. x 33 34 35 36 37 38 39 40 P(x) 0.02 0.06 0.10 0.20 0.24 0.26 0.10 0.02 (a) Find the probability that the random variable x is at most 38. Don't round. (b) Find the probability that the random variable x is at least 35. Don't round.
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The probability distribution of the random variable X is given in the following table. Random variable, x -2 -1 0 1 2 3 P(X = x) 0.10 0.15 0.05 0.20 0.15 0.35 Find the following probabilities. (a) P(X = 0)(b) P(X ≤ 0)(c) P(-1 < X ≤ 4)(d) P(X ≥ 1)
Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. y 0 1 2 3 4 p(y) 0.63 0.19 0.11 0.05 ? (a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.) p(4) = Calculate P(y ≤ 2), the probability that the carton contains at most two broken eggs. P(y ≤ 2) = Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs. P(y < 2) =
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A discrete random variable x has the the following probability distribution X 2 3 4 5 6 P(X=x) 3k2k2 3k2k2 3kk 2kk kk i) Find the value of k? ii) Find P[X>5][3.5<X<6.5]P[X>5][3.5<X<6.5]
X 1 2 3. A physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. He has the following probability distribution. 3 4 5 6 P(x) 0.35 0.20 0.15 0.10 0.05 x*P(x a. Define the random variable x. b. Define P(x), or the probability of x. c. Find the probability that a physics major will do post-graduate research for four years. P(x = 4) =_ d. Find the probability that a physics major will do post-graduate research for at most three years. P(x ≤ 3) =_ e. On average, how many years would you expect a physics major to spend doing post-graduate research?
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2. A random variable|x has the following probability distribution. Find the value of p and then evaluate the following probabilities: P(X 5) and P(0 < X < 6). Find the mean of the probability distribution. 1 3 4 6 17 P(X) 2p 2p 3p p2 2p2 7p? + p Value of p = P(X < 5) =. P(X 2 5) = P(0 < X < 5) = Mean (u) =
(1) The following table gives a probability distribution of a random variable X. F1 1 3 LValues of X Probabilities 0.4 0.4 0.1 0.1 The expectation of X is -1 0.4 0.5 1.5 N/A (Select One)

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