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Question # 10 A random variable (RV) x is uniformly-distributed from a to b. Given that:...
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Question # 8 A random variable (RV) x is uniformly-distributed from a to b. Given that the pdf of x, p(a x b) = 2; and, the median value of the RV is equal to: 5. Hence, determine the values of a and b. (Note: The median divides the distribution such that, cumulative probability to its left is equal to cumulative probability to...
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is a...
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is as follows: Px(x)-axexp(-ax) x 20 otherwise where α is a constant. Suppose y = log(x) and y is monotonic in the given range of X. Determine: (i) pdf of y; (ii) valid range of y; and, (iii) expected value of y. Answer hint:J exp(y) (b) Given that, the pdf, namely, fx(x) of a RV, x is uniformly distributed in the range (-t/2, +...
Let X be a uniformly distributed random variable on [0,1]. Then, X divides [0,1] into the...
Let X be a uniformly distributed random variable on [0,1]. Then, X divides [0,1] into the subintervals [0,X] and [x,1]. By symmetry, each subinterval has a mean length 0.5. Now pick one of the subintervals at random in the following way: Let Y be independent of X and uniformly distributed on [0,1], and pick the subinterval [0,X], or (X,1] that Y falls in. Let L be the length of the subinterval so chosen. What is the mean length of L...
X is a random variable exponentially distributed with mean Y, where Y is uniformly distributed on...
X is a random variable exponentially distributed with mean Y, where Y is uniformly distributed on the interval [0,2], Find P(X>2|Y>1) roblems:
X is a random variable exponentially distributed with mean Y, where Y is uniformly distributed on the interval [0,2], Find P(X>2|Y>1) roblems:
help asap 2. The random variable X is uniformly distributed in the interval [4,8). Find the...
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2. The random variable X is uniformly distributed in the interval [4,8). Find the probability density function for random variable Y if Y 6X 12 3. Two independent random variables X and y are given with their distribution laws: 0.2 0.4 0.1 0.9 0.7 0.1 p. Find the distribution law and mode of the random variable Z-5XY 0.2
1. Let U be a random variable that is uniformly distributed on the interval (0,1) (a)...
1. Let U be a random variable that is uniformly distributed on the interval (0,1) (a) Show that V 1 - U is also a uniformly distributed random variable on the interval (0,1) (b) Show that X-In(U) is an exponential random variable and find its associated parameter (c) Let W be another random variable that is uformly distributed on (0,1). Assume that U and W are independent. Show that a probability density function of Y-U+W is y, if y E...
7. Does there exist a random variable Y that is uniformly distributed on (a, b) for...
7. Does there exist a random variable Y that is uniformly distributed on (a, b) for a < b such that EYVar(Y)?
Let a random variable X be uniformly distributed between −1 and 2. Let another random variable...
Let a random variable X be uniformly distributed between −1 and 2. Let another random variable Y be normally distributed with mean −8 and standard deviation 3. Also, let V = 22+X and W = 13+X −2Y . (a) Is X discrete or continuous? Draw and explain. (b) Is Y discrete or continuous? Draw and explain. (c) Find the following probabilities. (i) The probability that X is less than 2. (ii) P(X > 0) (iii) P(Y > −11) (iv) P...
Assume random variable ? is uniformly distributed in the interval (−?/2 ,?⁄ 2]. Define the random...
Assume random variable ? is uniformly distributed in the
interval (−?/2 ,?⁄ 2]. Define the random variable ?=tan (?), where
tan (∙) denotes the tangent function. Note that the derivative of
tan (?) is 1/(cos (?)2) .
a) Find the PDF of ?.
b) Find the mean of ?
.Define the random variable ?=1/?.
c) Find the PDF of ?.
Assume random variable X is uniformly distributed in the interval (-1/2, 1/2). Define the random variable Y = tan(X), where...
Problem 9: Suppose X is a continuous random variable, uniformly distributed between 2 and 14. a....
Problem 9: Suppose X is a continuous random variable, uniformly distributed between 2 and 14. a. Find P(X <5) b. Find P(3<X<10) c. Find P(X 2 9)
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Question # 8 A random variable (RV) x is uniformly-distributed from a to b. Given that the pdf of x, p(a x b) = 2; and, the median value of the RV is equal to: 5. Hence, determine the values of a and b. (Note: The median divides the distribution such that, cumulative probability to its left is equal to cumulative probability to...
Question # A.4 (a) Given that probability density function (pdf of a random variable (RV), x is as follows: Px(x)-axexp(-ax) x 20 otherwise where α is a constant. Suppose y = log(x) and y is monotonic in the given range of X. Determine: (i) pdf of y; (ii) valid range of y; and, (iii) expected value of y. Answer hint:J exp(y) (b) Given that, the pdf, namely, fx(x) of a RV, x is uniformly distributed in the range (-t/2, +...
X is a random variable exponentially distributed with mean Y, where Y is uniformly distributed on the interval [0,2], Find P(X>2|Y>1) roblems:
X is a random variable exponentially distributed with mean Y, where Y is uniformly distributed on the interval [0,2], Find P(X>2|Y>1) roblems:
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2. The random variable X is uniformly distributed in the interval [4,8). Find the probability density function for random variable Y if Y 6X 12 3. Two independent random variables X and y are given with their distribution laws: 0.2 0.4 0.1 0.9 0.7 0.1 p. Find the distribution law and mode of the random variable Z-5XY 0.2
1. Let U be a random variable that is uniformly distributed on the interval (0,1) (a) Show that V 1 - U is also a uniformly distributed random variable on the interval (0,1) (b) Show that X-In(U) is an exponential random variable and find its associated parameter (c) Let W be another random variable that is uformly distributed on (0,1). Assume that U and W are independent. Show that a probability density function of Y-U+W is y, if y E...
7. Does there exist a random variable Y that is uniformly distributed on (a, b) for a < b such that EYVar(Y)?
Assume random variable ? is uniformly distributed in the
interval (−?/2 ,?⁄ 2]. Define the random variable ?=tan (?), where
tan (∙) denotes the tangent function. Note that the derivative of
tan (?) is 1/(cos (?)2) .
a) Find the PDF of ?.
b) Find the mean of ?
.Define the random variable ?=1/?.
c) Find the PDF of ?.
Assume random variable X is uniformly distributed in the interval (-1/2, 1/2). Define the random variable Y = tan(X), where...
Problem 9: Suppose X is a continuous random variable, uniformly distributed between 2 and 14. a. Find P(X <5) b. Find P(3<X<10) c. Find P(X 2 9)
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