In a new MOBA video game, the damage dealt by a character is a random variable, X, with cumulativedistribution function(x-1)²for 1 10a) Find the probability density function of X.b) Find the mean and variance of X.c) After buying and equipping the "Hextech Gauss Bow" , the damage dealt by the character is transformedto the random variable Y = 2X +5. Find the probability density function of Y.d) Using R, plot the probability density functions of X and Y on the same plot. Discuss the differencesbetween the distributions, in terms of range, mean and variance.e) Using R:i. By applying an appropriate transform of a uniform random variable, sample 50,000 observations fromX and produce a histogram of their distribution. Make sure to set your seed to your student ID beforeproceeding.ii. multiply each of your 50,000 observations in i. by 2 and add 5, and produce a histogram of thetransformed observations.iii. compare your histograms from i. and ii. with the probability distribution functions plotted in d).

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Answered: In a new MOBA video game, the damage…

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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In which probability distribution would a random variable XX have E(X)=λE(X)=λ?
2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1
In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine: (c) E(X)= i Round your answer to two decimal places (e.g. 98.76).
Please only solve number 8. Thank you tutor and God bless!
Compute the variance of the following probability distribution. If X is a random variable, then the variance is given by Var(X) = E (×²) – [E(X)]². k Pr(X= k) 0 0.1 1 0.3 2 0.5 3 0.1 Var(X) = (Type an integer or a decimal.)
An unfair die looks like an ordinary six-sided die but the outcomes are not equally likely. The probability distribution of the face value, XX, is as follows: xixi 1 2 3 4 5 6 Total P(X=xi)P(X=xi) 0.15 0.16 0.33 0.2 0.11 0.05 1 The expected value is computed, E[X]=3.11E[X]=3.11. To find the variance and standard deviation the following table was set up: xixi P(X=xi)P(X=xi) (xi−E[X])2(xi-E[X])2 (xi−E[X])2P(X=xi)(xi-E[X])2P(X=xi) 1 0.15 (1−3.11)2=(−2.11)2=4.4521(1-3.11)2=(-2.11)2=4.4521 4.4521⋅0.15=0.66784.4521⋅0.15=0.6678 2 (2−3.11)2=(−1.11)2=1.2321(2-3.11)2=(-1.11)2=1.2321 1.2321⋅0.16=0.19711.2321⋅0.16=0.1971 3 0.33 (3−3.11)2=(−0.11)2=(3-3.11)2=(-0.11)2= 0.0121⋅0.33=0.0040.0121⋅0.33=0.004 4 0.2 (4−3.11)2=(0.89)2=0.7921(4-3.11)2=(0.89)2=0.7921 0.7921⋅0.2=0.7921⋅0.2= 5 (5−3.11)2=(1.89)2=3.5721(5-3.11)2=(1.89)2=3.5721 3.5721⋅0.11=0.39293.5721⋅0.11=0.3929 6 0.05 8.3521⋅0.05=0.41768.3521⋅0.05=0.4176 E[X]=3.11E[X]=3.11 Total:…
QUESTION 4 The probability density function for the time taken to complete a 1-hour test (X) by students is given by a) b) c) Find the value of c. f(x) = {cx² + x ! ) 0≤x≤1 elsewhere Find the probability that a randomly selected student will finish in at least half an hour. Calculate the variance of X.
Given the following table, which corresponds to the values that a random variable X takes and its probability function p(x): xi 2 3 4 5 6 7 p(xi) 0.088 0.34 0.46 0.06 0.04 0.012 Calculate the distribution function (integral function) of x.

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