A random variable X has the following probability function,2 3 4 5 6178fongoniwoll P(x) a 3a 5aЗа7a 9a11a13а15a 17a1D2Determine the value of 'a'.

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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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A cigarette company wants to promoe thne sales of X's cigarettes (Brand) with special advertising campaign. Fifty out of every thousand cigarettes are rolled up in gold foil and randomly mixed with the regular (special king-sized, mentholated) cigarettes. The company offers to trade a new package of cigarettes for each gold cigarette a smoker finds in a package of Brand X. What is the probability that buyers of Brand X will find X = 0, 1, 2, 3, . gold cigarettes in a single package of 10 ? ...
Q1:Show that: If X1, X2, , Xn are independent random variables and X = X1 + X2 ++Xn, then Q2: What is the expectation and the variance of RV X, where X represents the out come throwing a die? Q3: Find the expectation and the variance of X, where X is binomial random variable X - Binomial (n, p), Var(X)? 1 Chapter 3 Let X be a discrete random variable with range Rx = {1, 2, 3, ...}. Q4: Suppose the PMF of X is given by 1 for k = 1, 2, 3, ... 2k Px (k) = a) Find and plot the CDF of X, Fx (a). b) Find P(1 < X < 3). Chapter 3 Functions of Random Variables Q5: Example. Let Rx = {0, T T 37 , such that 4'2 4. Find E[sin(X)]. Q6: A machine produces a defected items with a probability of 0.1. What is the probability that in a sample of three item will have at most one item defected? Q7: For any independent X, and Y random variables, E[XY]=E[X]E[Y]. Show that? Q8: Suppose RV X has the following PMF: p(0)=0.2, p(1)=0.5, p(2)=0.3. Find E[X], E[X^2], E[X]^2. 3 Chapter 3
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J 2 Uncorrelated random variables are not necessarily independent, however. A special situation occurs in the case of jointly Gaussian random variables. For the Gaussian case, uncorrelated random variables are also independent. I donot understand thses sentence. Please explain it through an example.
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2. A random variable X has the following probability distribution. 1 2 3 4 5 6 7 8 f(X) k 2k 3k | 4k 5k 6k 7k 8k Find the value of, (i) ´k (ii) P(X<2) (iii) P(2
a random variable has probability distribution: x= 0,1,2,3,4,5,6,7 and P(x) =0,k,2k,2k,3k,k*k.2k*k, 7k (k+1), the value of p(x<3)= O a. no one of them O b. 0.3 O c. 1
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- A random variable X has the following probability function, 2 3 4 5 6 7 8 P(x) 3a 5a 7a 9a 15a 17a a 11a 13a Determine the value of 'a'.