1. Suppose that X ( S )= { 1 , 3 , 4 , 6 }...
1. Suppose that X ( S )= { 1 , 3 , 4 , 6 } with P ( X =1)= P ( X =6)=0 . 1 and P ( X =3)= P ( X =4)=0 . 4.
Determine each of the following:
(a) The probability mass function of X .
(b) The cumulative distribution function of X .
(c) The expected value of X .
(d) The variance of X .
(e) The standard deviation of X
Homework Answers
math 1. Suppose that a weighted die is tossed. Let X denote the number of dots...
math
1. Suppose that a weighted die is tossed. Let X denote the number of dots that appear on the upper face of the die, and suppose that P(X = z) = (7-2)/20 for x = 1, 2, 3, 4, 5 and P(X = 6) = 0. Determine each of the following: 116 CHAPTER 4. DISCRETE RANDOM VARIABLES (a) The probability mass function of X (b) The cumulative distribution function of X (c) The expected value of X (d) The...
Ellen is taking 4 courses for the semester. She believes that the probability mass function for...
Ellen is taking 4 courses for the semester. She believes that
the probability mass function for X = the number of courses for
which she will get an A grade is given below.
k 0 1 2 3 4 ?(? = ?) 0.10 ? 0.40 0.15 0.05
a) What is the probability that Ellen gets at least 2 A’s?
(Write the probability sentence related) (3pts)
b) Complete the cumulative distribution function (cdf): (5pts) k
0 1 2 3 4 ?(?...
Question 4: Let X and Y be two discrete random variables with the following joint probability...
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
4. Suppose that X is a random variable having the following probability distri- bution function -...
4. Suppose that X is a random variable having the following probability distri- bution function - 0 if r<1 1/2 if 1 x <3 1 if z 2 6 (a) Find the probability mass function of X. (b) Find the mathematical expectation and the variance of X (c) Find P(4 X < 6) and P(1 < X < 6). (d) Find E(3x -6X2) and Var(3X-4).
Observers have noticed that the distribution function of X, which is the number of commercial vehicles...
Observers have noticed that the distribution function of X, which is the number of commercial vehicles that cross a certain toll bridge during a minute, is as follows: F(x)-0 for for for for x<0 0<= x <1 1<= x < 2 2<= x <3 0.20 0.50 0.70 0.85 for 3x<4 0.95 for 4<x<:5 1.00 for 5<= x < 6 a. Graph the (cumulative) distribution function (CDF) of X b. Find the probability (mass) function (PMF) of X. C. Graph the...
Q1: Suppose the probability density function of the magnitude X of a bridge (in newtons) is...
Q1: Suppose the probability density function of the magnitude X of a bridge (in newtons) is given by fx)-[e(1+3) sxs2 otherwise (a) Find the value of c. (b) Find the mean and variance (c) Find P(1 <x<2.25) (d) Find the cumulative distribution function.
Suppose that X is a continuous random variable with density pX(x) = ( Cx(1 − x)...
Suppose that X is a continuous random variable with density
pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if x < 0 or x > 1.
(a) Find C so that pX is a probability density function.
(b) Find the cumulative distribution of X.
(c) Calculate the probability that X ∈ (0.1, 0.9).
(d) Calculate the mean and the variance of X.
9.) Suppose that X is a continuous random variable with density C(1x) if E...
Let X = the headway between two randomly selected consecutive cars (sec). Suppose that in a...
Let X = the headway between two randomly selected consecutive cars (sec). Suppose that in a different traffic environment =, the distribution of time headway has the form: f(x) = {k/(x^5) if x >= 1, 0 if x <= 1 A: Determine the value of k for which f(x) is a legitimate pdf. B: Obtain the cumulative distribution function. C: Use the cdf form (b) to determine the probability that headway exceeds 2 sec and also the probability that headway...
function: Suppose the random variable X has the following cunulative distribution 0 if-00<z<-8 0.1 if 8-6...
function: Suppose the random variable X has the following cunulative distribution 0 if-00<z<-8 0.1 if 8-6 0.71 if -1Kz<5 Parts (a) through (d) below will be hand-graded. See instructions in Question O of this assignment. a. Draw the cumulative distribution function. b. Find and draw the pmf of X. c. What is the expected value of X? Submit Answer Tries o/s d. What is the variance of X? Submit Answer Tries 0/5 e. What is P(X 2.5)? Submit Answer Tries...
Suppose X is a random variable taking on possible values 1,2,3 with respective probabilities.4, .5, and...
Suppose X is a random variable taking on possible values 1,2,3 with respective probabilities.4, .5, and .1. Y is a random variable independent from X taking on possible values 2,3,4 with respective probabilities .3,.3, and 4. Use R to determine the following. a) Find the probability P(X*Y = 4) b) Find the expected value of X. c) Find the standard deviation of X. d) Find the expected value of Y. e) Find the standard deviation of Y. f) Find the...
math
1. Suppose that a weighted die is tossed. Let X denote the number of dots that appear on the upper face of the die, and suppose that P(X = z) = (7-2)/20 for x = 1, 2, 3, 4, 5 and P(X = 6) = 0. Determine each of the following: 116 CHAPTER 4. DISCRETE RANDOM VARIABLES (a) The probability mass function of X (b) The cumulative distribution function of X (c) The expected value of X (d) The...
Ellen is taking 4 courses for the semester. She believes that
the probability mass function for X = the number of courses for
which she will get an A grade is given below.
k 0 1 2 3 4 ?(? = ?) 0.10 ? 0.40 0.15 0.05
a) What is the probability that Ellen gets at least 2 A’s?
(Write the probability sentence related) (3pts)
b) Complete the cumulative distribution function (cdf): (5pts) k
0 1 2 3 4 ?(?...
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
4. Suppose that X is a random variable having the following probability distri- bution function - 0 if r<1 1/2 if 1 x <3 1 if z 2 6 (a) Find the probability mass function of X. (b) Find the mathematical expectation and the variance of X (c) Find P(4 X < 6) and P(1 < X < 6). (d) Find E(3x -6X2) and Var(3X-4).
Observers have noticed that the distribution function of X, which is the number of commercial vehicles that cross a certain toll bridge during a minute, is as follows: F(x)-0 for for for for x<0 0<= x <1 1<= x < 2 2<= x <3 0.20 0.50 0.70 0.85 for 3x<4 0.95 for 4<x<:5 1.00 for 5<= x < 6 a. Graph the (cumulative) distribution function (CDF) of X b. Find the probability (mass) function (PMF) of X. C. Graph the...
Q1: Suppose the probability density function of the magnitude X of a bridge (in newtons) is given by fx)-[e(1+3) sxs2 otherwise (a) Find the value of c. (b) Find the mean and variance (c) Find P(1 <x<2.25) (d) Find the cumulative distribution function.
Suppose that X is a continuous random variable with density
pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if x < 0 or x > 1.
(a) Find C so that pX is a probability density function.
(b) Find the cumulative distribution of X.
(c) Calculate the probability that X ∈ (0.1, 0.9).
(d) Calculate the mean and the variance of X.
9.) Suppose that X is a continuous random variable with density C(1x) if E...
function: Suppose the random variable X has the following cunulative distribution 0 if-00<z<-8 0.1 if 8-6 0.71 if -1Kz<5 Parts (a) through (d) below will be hand-graded. See instructions in Question O of this assignment. a. Draw the cumulative distribution function. b. Find and draw the pmf of X. c. What is the expected value of X? Submit Answer Tries o/s d. What is the variance of X? Submit Answer Tries 0/5 e. What is P(X 2.5)? Submit Answer Tries...
Suppose X is a random variable taking on possible values 1,2,3 with respective probabilities.4, .5, and .1. Y is a random variable independent from X taking on possible values 2,3,4 with respective probabilities .3,.3, and 4. Use R to determine the following. a) Find the probability P(X*Y = 4) b) Find the expected value of X. c) Find the standard deviation of X. d) Find the expected value of Y. e) Find the standard deviation of Y. f) Find the...
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