1. Consider a discrete random variable, X, where the outcome of this random variable is determined...
1. Consider a discrete random variable, X, where the outcome of this random variable is determined by throwing a 6-sided die. X takes on integer values 1,2,…,6. The die is fair. That is, P(X=1)= P(X=2)=…= P(X=6).
i. Draw the probability distribution function for this random variable. Carefully label the graph.
ii. Draw the cumulative distribution function for X.
iii. Calculate the following: P(X=4) P(X≠5) P(X=1 or X=6) P(X4) E(X) Var(X) sd(X)
iv. Consider the random variable Y where the outcome of Y is determined by throwing a second, fair, 6-sided die. Now consider the joint distribution of X and Y. Calculate the following: P(X=1 and Y=1) P(X≠1 and Y≠2) P(Y=2|X=1) Cov(X,Y)
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1. Consider a discrete random variable, X, where the outcome of
this random variable is determined...
Let X be a discrete random variable with 1 P(X = 1) = P(X = 2)...
Let X be a discrete random variable with 1 P(X = 1) = P(X = 2) = P(X = 3) = P(X= 4) = Then given X = x, we roll a fair 4-sided die 3 times. (The 4-sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y|X]. Hint: Remember E[Y | X] is a random variable, so X will be part...
Let X be a discrete random variable with P(X = 1) = 1 4 1 P(X...
Let X be a discrete random variable with P(X = 1) = 1 4 1 P(X = 2) = 8 1 P(X = 3) = 2 P(X = 4) = 8 Then given X = x, we roll a fair 4-sided die x times. (The 4- sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y| X]. Hint: Remember E|Y|X] is a...
1. (6 pts) Consider a non-negative, discrete random variable X with codomain {0, 1, 2, 3,...
1. (6 pts) Consider a non-negative, discrete random variable X with codomain {0, 1, 2, 3, 4, 5, 6} and the following incomplete cumulative distribution function (c.d.f.): 0 0.1 1 0.2 2 ? 3 0.2 4 0.5 5 0.7 6 ? F(x) (a) Find the two missing values in the above table. (b) Let Y = (X2 + X)/2 be a new random variable defined in terms of X. Is Y a discrete or continuous random variable? Provide the probability...
Consider a discrete random variable X with the probability mass function p X ( x )...
Consider a discrete random variable X with the probability mass function p X ( x ) = x/C , x = 3, 4, 5, 6, 7, zero elsewhere. consider Y = g( X ) = 100/(x^2+1) . b) Find the probability distribution of Y.
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2,...
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2, 3,..The moment generating function for this kind of random variable is M(t)Pe 1-(1-P)et. (a) What is E(X)? O p(1-P) 1-P (a) What is Var(x)? 1-p p2 p(1-P) O p(1-P) o -p
1. The probability distribution of a discrete random variable X is given by: P(X =-1) =...
1. The probability distribution of a discrete random variable X is given by: P(X =-1) = 5, P(X = 0) = and P(X = 1) = ? (a) Compute E[X]. (b) Determine the probability distribution Y = X2 and use it to compute E[Y]. (c) Determine E[x2] using the change-of-variable formula. (You should match your an- swer in part (b). (d) Determine Var(X).
2. Consider a discrete random variable X with mean u = 4.9 and probability distribution function...
2. Consider a discrete random variable X with mean u = 4.9 and probability distribution function p(x) given in the table below. Find the values a and b and calculate the variance o p(x) 0.25 5 6 0.35
Problem 4 Let X be the following discrete random variable: P(X-1) = P(X = 0) =...
Problem 4 Let X be the following discrete random variable: P(X-1) = P(X = 0) = P(x-1) Let Y-X2. Show that cov(X, Y) 0, but X and Y are not independent random variable.
The distribution function of the discrete random variable X is given by; Compute: 1 1. P(X...
The distribution function of the discrete random variable X is given by; Compute: 1 1. P(X 2) 2. P(X 3| X 3. Е [X] 4. Var (X F (x) = 4 2) 2 x 3 < 3 x< 3.5 wwwwww 10 1, x 3.5
the probability distribution function for the discrete random variable where X is equal to the number...
the probability distribution function for the discrete random variable where X is equal to the number of red lights drivers typically run in year follows. x 1,2,3, p(x) 0.70, 0.12 , 0.02 , 0.16 what is the mean of this discrete random variavle?
Let X be a discrete random variable with 1 P(X = 1) = P(X = 2) = P(X = 3) = P(X= 4) = Then given X = x, we roll a fair 4-sided die 3 times. (The 4-sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y|X]. Hint: Remember E[Y | X] is a random variable, so X will be part...
Let X be a discrete random variable with P(X = 1) = 1 4 1 P(X = 2) = 8 1 P(X = 3) = 2 P(X = 4) = 8 Then given X = x, we roll a fair 4-sided die x times. (The 4- sided die is equally likely to come up a 1, 2, 3, or 4). Let y be the number of times we roll a 1. (a) Find E[Y| X]. Hint: Remember E|Y|X] is a...
1. (6 pts) Consider a non-negative, discrete random variable X with codomain {0, 1, 2, 3, 4, 5, 6} and the following incomplete cumulative distribution function (c.d.f.): 0 0.1 1 0.2 2 ? 3 0.2 4 0.5 5 0.7 6 ? F(x) (a) Find the two missing values in the above table. (b) Let Y = (X2 + X)/2 be a new random variable defined in terms of X. Is Y a discrete or continuous random variable? Provide the probability...
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2, 3,..The moment generating function for this kind of random variable is M(t)Pe 1-(1-P)et. (a) What is E(X)? O p(1-P) 1-P (a) What is Var(x)? 1-p p2 p(1-P) O p(1-P) o -p
1. The probability distribution of a discrete random variable X is given by: P(X =-1) = 5, P(X = 0) = and P(X = 1) = ? (a) Compute E[X]. (b) Determine the probability distribution Y = X2 and use it to compute E[Y]. (c) Determine E[x2] using the change-of-variable formula. (You should match your an- swer in part (b). (d) Determine Var(X).
2. Consider a discrete random variable X with mean u = 4.9 and probability distribution function p(x) given in the table below. Find the values a and b and calculate the variance o p(x) 0.25 5 6 0.35
Problem 4 Let X be the following discrete random variable: P(X-1) = P(X = 0) = P(x-1) Let Y-X2. Show that cov(X, Y) 0, but X and Y are not independent random variable.
The distribution function of the discrete random variable X is given by; Compute: 1 1. P(X 2) 2. P(X 3| X 3. Е [X] 4. Var (X F (x) = 4 2) 2 x 3 < 3 x< 3.5 wwwwww 10 1, x 3.5
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