8. A random variable X has the following probability distribution:5 673k k² 2k² 7k²+kX01234P(X)0K2k 2kDetermine(i) k(ii) P(X < 3)31

Step 1:(i)We know that total probability should be…

Answered: 8. A random variable X has the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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W is a random variable with probabilities for w= 0,1 P(W = w) = {2h + k for w= 2 %3D 3k for w= 3,4 7 find the values of h and k. 10 (а) If P(W <2) = (b) Construct a probability distribution table for W. 4.
3. A discrete random variable has the the following probability distribution 1. 2 4 7. 8 6. P(X=x) 2k 5k 7k 6k 11k 9k 3k k 10k o) Find the value of k? b) Find E(5X+3)?
24. Use the probability distribution to complete parts (a) through (d) below. The probability distribution of number of televisions per household in a small town X 0 3 P(x) 0.03 0.54 (a) Find the probability of randomly selecting a household that has one or two televisions. The probability is (Type an integer or a decimal. Do not round.) (b) Find the probability of randomly selecting a household that has two or more televisions. 1 0.11 2 0.32 The probability is (Type an integer or a decimal. Do not round.) (c) Find the probability of randomly selecting a household that has between one and three televisions, inclusive. The probability is (Type an integer or a decimal. Do not round.) (d) Find the probability of randomly selecting a household that has at most two televisions. The probability is (Type an integer or a decimal. Do not round.)
Q P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5
5. The probability distribution of discrete random variable X is given by k for x = 1, 2, 3 x +1 P(X = x) %3D
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(i) Construct the probability distribution table (ii) What is the probability that there will be at most 1 car in the parking lot? (iii) Calculate the expected number of cars in the parking lot at midday
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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8. A random variable X has the following probability distribution: 5 6 7 3k k² 2k² 7k²+k X 0 1 2 34 P(X) 0 K 2k 2k Determine (i) k (ii) P(X < 3) 31