Given the probability distributions shown to the right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B. |
Distribution A |
Distribution B |
||||
---|---|---|---|---|---|---|
x Subscript ixi |
P(Xequals=x Subscript ixi ) |
x Subscript ixi |
P(Xequals=x Subscript ixi ) |
|||
0 |
0.480.48 |
0 |
0.050.05 |
|||
1 |
0.240.24 |
1 |
0.090.09 |
|||
2 |
0.140.14 |
2 |
0.140.14 |
|||
3 |
0.090.09 |
3 |
0.240.24 |
|||
4 |
0.050.05 |
4 |
a) Expected value of A E(A)= x*p(x)= 0*0.48+1*0.24+2*0.14+3*0.09+4*0.05= 0.99
E(B) = (0*0.05+1*0.09+2*0.14+3*0.24)= 1.09
b) V(A)= E(A^2)+{E(A)}^2
E(A^2)= = (0)^2*0.48 +(1)^2*0.24 +(2)^2*0.14+(3)^2*0.09+(4)^2*(0.05) =2.41
V(A)= 2.41-(0.99)^2
V(A)= 2.41-0.98
V(A)=1.43
STD (A)= SQRT(1.43)= 1.196
V(B)= E(B^2)+{E(B)}^2
E(B^2)= = (0)^2*0.05 +(1)^2*0.09 +(2)^2*0.14+(3)^2*0.24= 2.81
V(B)= 2.81-(1.09)^2= 2.81-1.19= 1.62
STD(B)= SQRT(1.62)= 1.27
c) In A distribution P(X>=3)= 0.09+0.05= 0.14
In B distribution P(X>=3)=0.24
THERE IS MORE VARIABILITY IN DISTRIBUTION B THAN IN A
Given the probability distributions shown to the right, complete the following parts. a. Compute the expected...
Given the probability distributions shown to the right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B. Distribution A: xi Distribution A: P(X=xi) Distribution B: xi Distribution B: P(X=xi) 0 0.02 0 0.49 1 0.09 1 0.24 2 0.16 2 0.16 3...
Problem 1 * o - nm + Given the following probability distributions: Distribution C Distribution D P(x) 0.20 0.20 0.20 0.20 0.20 xo - nm + P(x) 0.10 0.20 0.40 0.20 0.10 a. Compute the expected value for each distribution Compute the standard deviation for each distribution Compare the results of distributions C and D C.
section 16 probability distributions and expected values activity Section 16 Probability Distributions and Expected Values Activity 2 The following are probability distributions for variable x. Answer the given questions for each: 1. Z less than 4.W {(x) 0.1 0.1 0.2 02 20 a) P(x = 9) b) P(x = 20) c) P( x3) d) The mean for variable x e) The Standard deviation for variable x 120
Consider the probability distribution shown below. x 0 1 2 P(x) 0.45 0.20 0.45 (a) Compute the expected value of the distribution. (b) Compute the standard deviation of the distribution Compute the standard deviation of the distribution. (Round your answer to four decimal places.)
Consider the discrete probability distribution to the right. Complete parts a and b below. a. Calculate the mean of this distribution u = 2.44 (Type an integer or a decimal.) b. Calculate the standard deviation of this distribution G= (Round to three decimal places as needed.) Vuesuon Help Consider the discrete probability distribution to the right. Complete parts a and b below Outcome Probability 0.31 0.24 015 0.30 a. Calculate the mean of this distribution * 2.44 (Type an integer...
2) Consider a random variable with the following probability distribution: P(X-0)-0., Px-1)-0.2, PX-2)-0.3, PX-3) -0.3, and PX-4)-0.1 A. Generate 400 values of this random variable with the given probability distribution using simulation. B. Compare the distribution of simulated values to the given probability distribution. Is the simulated distribution indicative of the given probability distribution? Explain why or why not. C. Compute the mean and standard deviation of the distribution of simulated values. How do these summary measures compare to the...
9. A probability distribution is shown to the right. By hand, find the mean and standard deviation for the random variable, x, where x represents the number of bicycles per household in a town of 1000 households. (Use the easier formula for standard deviation!) x P(x) 0 0.125 1 0.428 2 0.256 3 0.108 4 0.083 Mean :___________ Standard Deviation :___________
Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 0 3 Probability 0.268 0.305 0.240 0.140 2 O 4 0.036 5 0.011 (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.) The standard deviation is (Round to one decimal place as needed.) (b) Interpret the...
Complete parts (a) and (b) below. The number of dogs per household in a small town x P(x) 0 0.674 1 0.199 2 0.083 3 0.025 4 0.012 5 0.007 (a) Find the mean, variance, and standard deviation of the probability distribution. Find the mean of the probability distribution. Find the variance of the probability distribution. Find the standard deviation of the probability distribution. (b) Interpret the results in the context of the real-life situation. A.A household on average has...
Consider the probability distribution shown below. x 0 1 2 P(x) 0.05 0.80 0.15 Compute the expected value of the distribution. Compute the standard deviation of the distribution. (Round your answer to four decimal places.)