Question

Let f(x)=(1/2)(x/5), x=1,2,3,4 Hint: Calculate F(X).

Find; (a) P(X=2) , (b) P(X≤3) , (c) P(X>2.5), (d) P(X≥1), (e) mean and variance, (f) Graph F(x)

Answer #1

Let X be a random variable with pdf f(x)=12,
0<x<2.
a) Find the cdf F(x).
b) Find the mean of X.
c) Find the variance of X.
d) Find F (1.4).
e) Find P(12<X<1).
f) Find PX>3.

Let X ∼ B(5, 0.3). Determine:
(b) P(X < 2);
(c) P(X > 2);
Let X ∼ P0(2.1). Determine:
(a) P(X = 5);
(b) P(X < 3);
(c) P(X ≥ 3);
(d) E(X);
(e) var(X).

1. Find
a. P(Z=-1.01)
b. P(Z>10)
c. P(-1.5<Z<2)
d. P(-2.58<Z)
e. P(Z<3.15)
f. The 30th percentile of Z
g. The z value with 12% area to its right.
2. If X is normally distributed with a mean of 5.6 and a
variance of 27, find
a. P(X<2)
b. P(-2.5<X<7.2)
c. The 80th percentile of X

. Find
a. P(Z=-1.01)
b. P(Z>10)
c. P(-1.5<Z<2)
d. P(-2.58<Z)
e. P(Z<3.15)
f. The 30th percentile of Z
g. The z value with 12% area to its right.
2. If X is normally distributed with a mean of 5.6 and a
variance of 27, find
a. P(X<2)
b. P(-2.5<X<7.2)
c. The 80th percentile of X

Let S = {a, b, c, d, e, f} with P(b) = 0.21, P(c) = 0.11, P(d) =
0.11, P(e) = 0.18, and P(f) = 0.19. Let E = {b, c, f} and F = {b,
d, e, f}. Find P(a), P(E), and P(F).

Let X be a r.v with pmf p(x) = c( 2 /3 )^ x , x = 0, 1, 2, 3,
... (infinitely many values of x)
(a) Find the constant c. (b) With the constant you find in (a),
find the mean E(X)

Let f(x) = x^2 + 1, x ∈ [2, 7]. Let P = {2,4,5,7}.
Find L(f,P) and U(f,P).

a = [-5, -3, 2] b = [1, -7, 9] c = [7, -2, -3] d = [4, -1, -9,
-3] e = [-2, -7, 5, -3]
a. Find (d) (e)
b. Find (3a) (7c)
c. Find Pe --> d
d. Find Pc --> a +2b
ex. C = |x|(xy/xy) C = xy/|x|
ex. P x --> y = Cux = C(xy/x) (1/|x|) (x) =( xy/yy)(y)

Let X = {1, 2, 3} and Y = {a, b, c, d, e}.
(1) How many functions f : X → Y are there?
(2) How many injective functions f : X → Y are there?
(3) What is a if (x + 2)10 = x 10 + · · · + ax7 + · · · + 512x +
1024?

1. Let X be a discrete random variable with the probability mass
function P(x) = kx2 for x = 2, 3, 4, 6.
(a) Find the appropriate value of k.
(b) Find P(3), F(3), P(4.2), and F(4.2).
(c) Sketch the graphs of the pmf P(x) and of the cdf F(x).
(d) Find the mean µ and the variance σ 2 of X. [Note: For a
random variable, by definition its mean is the same as its
expectation, µ = E(X).]

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