Question

Let ?, ?, and ? be independent random variables, uniformly distributed over [0,5], [0,1] , and [0,2] respectively. What is the probability that both roots of the equation ??^2+??+?=0 ar

e real?

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.S read careful, I had already waste a chance to post question in this

Answer #1

1 point) Let A, B, and C be independent random variables,
uniformly distributed over [0,5], [0,15], and [0,2] respectively.
What is the probability that both roots of the equation Ax2+Bx+C=0
are real?

Let A, B, and C be independent random variables, uniformly
distributed over [0,3], [0,2], and [0,4] respectively. What is the
probability that both roots of the equation Ax2 +Bx+C=0
are real?
The answer is NOT 1/24 nor 7.2981/24 nor .304.

Let X1, X2, X3 be independent random variables, uniformly
distributed on [0,1]. Let Y be the median of X1, X2, X3 (that is
the middle of the three values). Find the conditional CDF of X1,
given the event Y = 1/2. Under this conditional distribution, is X1
continuous? Discrete?

Let Xi, i = 1, 2..., 48, be independent random variables that
are uniformly distributed on the interval [-0.5, 0.5].
(a) Find the probability Pr(|X1|) < 0.05
(b) Find the approximate probability P (|Xbar| ≤ 0.05).
(c) Determine an approximation of a such that P(Xbar ≤ a) =
0.15

Let X1,...,X99 be independent random variables, each one
distributed uniformly on [0, 1]. Let Y denote the 50th largest
among the 99 numbers. Find the probability density function of
Y.

Let U,V be i.i.d. random variables uniformly
distributed in [0,1]. Compute the following quantities:
E[|U−V|]=
P(U=V)=
P(U≤V)=

1.if a is uniformly distributed over [−12,24], what is the
probability that the roots of the equation x2+ax+a+24=0 are both
real?
Hint: The roots are real if the discriminant in the quadratic
formula is positive.
2.The time (in minutes) between arrivals of customers to a post
office is to be modelled by the Exponential distribution with mean
.38. Please give your answers to two decimal places.
Part a)
What is the probability that the time between consecutive customers
is less...

X and Y are independent and identically distributed variables
uniform over [0,1]. Find PDF of A=Y/X

1) Let the random variables ? be the sum of independent Poisson
distributed random variables, i.e., ? = ∑ ? (top) ?=1(bottom) ?? ,
where ?? is Poisson distributed with mean ?? .
(a) Find the moment generating function of ?? . (b) Derive the
moment generating function of ?. (c) Hence, find the probability
mass function of ?.
2)The moment generating function of the random variable X is
given by ??(?) = exp{7(?^(?)) − 7} and that of ?...

Suppose that X and Y are independent Uniform(0,1) random
variables. And let U = X + Y and V = Y .
(a) Find the joint PDF of U and V
(b) Find the marginal PDF of U.

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