Question

Suppose that X is uniformly distributed on the interval [0,5], Y is uniformly distributed on the interval [0,5], and Z is uniformly distributed on the interval [0,5] and that they are independent.

a)find the expected value of the max(X,Y,Z)

b)what is the expected value of the max of n independent random variables that are uniformly distributed on [0,5]?

c)find pr[min(X,Y,Z)<3]

Answer #1

Suppose that X is uniformly distributed on the interval [0,10],
Y is uniformly distributed on the interval [0,10], and Z is
uniformly distributed on the interval [0,10] and that they are
mutually independent.
a)find the expected value of the min(X,Y,Z)
b)find the standard deviation of the min(X,Y,Z)

The random variable X is uniformly distributed in the interval
[0, α] for some α > 0. Parameter α is fixed but unknown. In
order to estimate α, a random sample X1, X2, . . . , Xn of
independent and identically distributed random variables with the
same distribution as X is collected, and the maximum value Y =
max{X1, X2, ..., Xn} is considered as an estimator of α.
(a) Derive the cumulative distribution function of Y .
(b)...

Suppose that X is a random variable uniformly distributed over
the interval (0, 2), and Y is a random variable uniformly
distributed over the interval (0, 3). Find the probability density
function for X + Y .

Included all steps. Thanks
The random variable X is uniformly distributed in the interval
[0, α] for some α > 0.
Parameter α is fixed but unknown. In order to estimate α, a
random sample X1, X2, . . . , Xn of independent and identically
distributed random variables with the same distribution as X is
collected, and the maximum value Y = max{X1, X2, ..., Xn} is
considered as an estimator of α.
(a) Derive the cumulative distribution function...

X is uniformly distributed on the interval (0, 1), and Y is
uniformly distributed on the interval (0, 2). X and Y are
independent. U = XY and V = X/Y .
Find the joint and marginal densities for U and V .

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?

Suppose that X ∼ Unif[0, 3] and Y is independent of X and
exponentially distributed with rate 2.
Find the pdf of
(a) max{X,Y}. (b) min{X,Y}.

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

Consider n independent variables, {X1, X2, . . . , Xn} uniformly
distributed over the unit interval, (0, 1). Introduce two new
random variables, M = max (X1, X2, . . . , Xn) and N = min (X1, X2,
. . . , Xn).
(A) Find the joint distribution of a pair (M, N).
(B) Derive the CDF and density for M.
(C) Derive the CDF and density for N.
(D) Find moments of first and second order for...

Let Y1,Y2.....,Yn be independent ,uniformly distributed random
variables on the interval[0,θ].，Y(n)=max(Y1,Y2,....,Yn)，which is
considered as an estimator of θ. Explain why Y is a good estimator
for θ when sample size is large.

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