Let X be the number of random number of cars and the Y be the number of buses per signalcycle at a proposed left turn lane is displayed in the accompanying joint probability table.YX/Y120.0250.0150.01010.0500.0300.02020.1250.0750.05030.1500.0900.06040.1000.0600.0400.0500.0300.020Find E(X), E(Y), Var(X), Var(Y), o(x), , o(v), marginal density for x and yAre X and Y independent, show your solutionFind the correlation between X and Y variable and interpret your findings, show yoursolution.

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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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P(x) 0.029 Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. 1 0.157 0.314 0.314 0.157 5 4 0.029 O D. No, the sum of all the probabilities is not equal to 1. O E. No, not every probability is between 0 and 1 inclusive. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. А. child(ren) (Round to one decimal place as needed.) O B. The table does not show a probability distribution.
The discrete random variable X has the following probability distribution: -10 0 10 p(x) 0.20 0.40 .10 Which one of the following correctly gives the value of the mean and standard deviation of X? OH = 0.5, o = 37.5 OH = 2.25, o = 37.25 OH = 0.5, o = 6.10 OH= 2.25, o = 6.10 OH= 0.5 o = 37.25
It is assumed that the X chance variable shows a lognormal distribution with parameters μ = 0 and σ = 2. So what's the probability P(10 < X < 50) ?
The graph of the discrete probability to the right represents the number of live births by a mother 47 to 52 years old who had a live birth in 2015. Complete parts (a) through (d) below. 0.301 0.25 E0 20- 8 0.15 0270 0 237 O112 0103 20.10- 0.05- 000 Number of Live Births (a) What is the probability that a randomly selected 47- to 52-year-old mother who had a Iive birth in 2015 has had her fourth live birth in that year? |(Type an integer or a decimal) (b) What is the probability that a r omly selected 47- to 52-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? (Type an integer or a decimal.) (c) What is the probability that a randomly selected 47- to 52-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year? (Type an integer or a decimal.) (d) If a 47- to 52-year-old mother who had a live birth in 2015 is randomly selected, how many live births would you expect the mother to have had? (Round to one…
ACTIVITY B. Find the variance and standard deviation of each probability distributions. You may use the space provide below. 1 2 3 1. P(x) 0.10 0.45 0.25 0.20 X 1 2 3 4 P(x) 0.11 0.22 0.33 0.25 0.09 2.
VERSION 1 Q. 1 Let X be the number of bugs in the first draft of a piece of software, and let Y be the number of bugs remaining in the second draft of the same software. Their joint probability mass function is given by the following table: Y 1 3 0.03 0.11 0.09 0.08 1 0.05 0.12 K 0.04 0.04 0.06 0.08 0.09 021 (i) Obtain K so that it is the joint probability mass function;
Use n=10 and p=0.6 to complete parts (a) through (d) below.
The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. p(x, у) 1 2 0.015 0.010 0.025 1 0.030 0.020 0.050 2 0.075 0.050 0.125 3 0.090 0.060 0.150 4 0.060 0.040 0.100 0.030 0.020 0.050 (a) What is the probability that there exactly one car and exactly one bus during a cycle? (b) What is the probability that there is at most one car and at most one bus during a cycle? (c) What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) P(exactly one bus) = (d) Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflow during a cycle? (e) Are X and Y independent rv's? Explain. Yes, because p(x, y) = Px(x) · Py(y). Yes, because p(x, y) ± Px(x) · py(y). No, because p(x, y) = Px(x) · Py(Y). No, because p(x, y) # Px(x) · Py(y).
The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. y 1 p(x, y) 0 1 0.030 0.020 50 X 3 0.090 0.060 4 0.060 0.040 2 0 0.015 0.010 0.025 0.050 2 0.075 0.050 0.125 0.150 0.100 5 0.030 0.020 0.050 (a) What is the probability that there is exactly one car and exactly one bus during a cycle? 0.020 (b) What is the probability that there is at most one car and at most one bus during a cycle? 0.075 (c) What is the probability that there is exactly one car during a cycle? Exactly one bus? P(exactly one car) = 0.220 x P(exactly one bus) = 0.200 (d) Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflow during a cycle? 0.985 X (e) Are X and Y independent rv's? Explain. O Yes, because p(x, y) = P(x) Py(Y). O Yes, because p(x, y) = Px(x) • P₂(Y). # ● No, because p(x, y) = Px(x) •…
The graph of the discrete probability to the right represents 0.30- the number of live births by a mother 49 to 52 years old who had a live birth in 2015. Complete parts (a) through (d) below. 0.258 0.25- 0.232 0.20- 0.15- 0.10- 0.169 0.113 0.099 0.05- 0.031 0.041 0.057 0.00- Number of Live Births
Calculate the expected value of X, E(X), for the given probability distribution. x 1 2 3 4 P(X = x) 0.2 0.1 0.6 0.1 E(X) =
Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5, −1, 0, 2, and 4. Value x of X -5 -1 0 2 4 X P ( X = x) 0.23 0.18 0.24 15 .20 Ś

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