Question 3. Suppose that the random variable X is defined as X = 0.6X1 + 0.3X2 +0.1X3, where the probability distributions of the independent random variables X1, X2, and X3 are fx, (x) 0.1 0.95-z, %3D fx, (x) = 0.4 0.6" and fx, (x) = (* ) 0.6 0.45-z x 0, 1,... ,5. a) Evaluate the mean of X. b) Evaluate the variance of X.

Question 3. Suppose that the random variable X is defined as X = 0.6X1 + 0.3X2 +0.1X3, where the probability distributions of the independent random variables X1, X2, and X3 are fx, (x) 0.1 0.95-z, %3D fx, (x) = 0.4 0.6" and fx, (x) = (* ) 0.6 0.45-z x 0, 1,... ,5. a) Evaluate the mean of X. b) Evaluate the variance of X.

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...

See similar textbooks

Similar questions

Suppose the probability function for x is such that p(x=1)=0.3, p(x=2)=0.4 and p(x=3)=0.3. What is the variance of x ?
(a) Let X1, X2, X3 be random variables with the same variance variance o?. Then, the vari- o2 ance of X = Xi+X2+X3 will necessarily be 3. (i) if the X;'s are all normally distributed; (ii) always; (iii) if the X,'s are independent of each other3; (iv) if the X,'s are identically distributed. i.i.d. (b) If X1, X2, ..., X, N(u, o²), then as the sample size n increases, the standard deviation of X ΣΧ, n (i) increases; (ii) stays the same; (iii) decreases; (iv) increases or decreases depending on the sign of o?. (c) The interquartile range is a better measure of dispersion in data than the standard devia- tion when (i) the standard deviation and mean are not in the same unit; (ii) there are outliers; (iii) the variance and the interquartile range are in the same unit; (iv) the data is bimodal. MacBook Pro
В2. (a) Given the probability Venn diagram below for the two Events A and B find the probabilities: 0.6 0.5 A 0.2 (i) (ii) (iii) Pr( A 'OR' B) Pr( Not-A 'AND' Not-B) Pr( Not-A "OR' Not-B) (b) A random sample from a population of X with unknown mean but a known variance, o = 400, gives the following data: sample size, n= 125, Ex= 1750. (i) Give a point estimate of the population mean, u. (ii) Is this estimate biased or not. Give a reason. (ii) Derive a 95% confidence interval for the population mean, µ.
A particle executes an unrestricted simple random walk on the line with p=0.7 and q=0.3. Its position at time n is represented by the random variable Xn, n = 0, 1,...; Xo = 0. (a) Calculate the values of the following probabilities. (i) P(X5 = -2) (ii) P(X6 = 2) (b) Calculate the probability that the particle returns to its starting point for the first time after 8 steps. (c) After the particle has been moving for some time, it is observed to be located at the point +3. (i) Calculate the probability that the particle will ever return to the origin from the point +3. (ii) Calculate the probability that starting from the point +3, the particle will visit the point +8 without first visiting the origin.
Suppose a random variable X is best described by a uniform probability distribution with range 0 to 6. Find the value of a that makes the following probability statements true. (a) P(X a) = 0.79 a = (d) Р(X > а) — 0.13 a = (e) P(2.61 < X < a) = 0.03 %3D
In which probability distribution would a random variable XX have E(X)=λE(X)=λ?
МАТH1208 QUESTION 2 А. The table below shows the probability distribution of the likelihood of the number of SUVS in a household in Forest Hill, St Andrew. Number of 2 3 SUVS (x) P(X = x) 0.05 0.12 0.60 0.20 Find: i. The value of 'c' ( the probability of 4 SUVS in a household) ii. The expected value [E(X) ], the mean value of SUVS in a household iii. The variance iv. standard deviation of SUVS in a household
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
34. Suppose that X is a random variable with MGF M(t) = (1/8)e + (1/4)e + (5/8)e. (a) What is the distribution of X? (b) What is P[X= 2]?
Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random variable with CDF F(x) = 1 − e-x/3 x ≥ 0 What is the probability that the battery lasts between 12 to 15 months?
10. Two random variables X and Y take on the values i and 2 with probability 1/2' (i = 1,2, ...). Show that the probabilities sum to one. Find the expected value of X and Y.
16) number of medical tests that a patient will have on entering a hospital is a random variable X which can take on the values 0, 1, 2, 3, and 4. If P(X 2)=0.43, find P(X = 3).