Question

**5. Let x be a random variable with the following
probability distribution.**

**x P(x)**

**1 0.6**

**5 0.4**

**Consider a sample of size 3 from the population, and let
x be the sample mean. Construct a probability distribution for
x.**

Not sure how this was answered

correct Answer

**x P(x)**

**1 .216**

**7/3 .432**

**11/3 .288**

**5 .064**

Answer #1

x P(x)

1 0.216

7/3 0.432

11/3 0.288

5 0.064

1. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate E(X)
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
2. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate the variance of X
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
3. Given a discrete random variable, X...

Let X be a random variable with the following probability
distribution: Value x of X P=Xx 1 0.15 2 0.55 3 0.05 4 0.15 5 0.10
Find the expectation EX and variance Var X of X .

Let X be a random variable with the following probability
distribution:
Value x of X P(X=x)
4 0.05
5 0.30
6 0.55
7 0.10
Find the expectation E (X) and variance Var (X) of X. (If
necessary, consult a list of formulas.)
E (x) = ?
Var (X) = ?

let X be a binomial random variable with n=8 and p=0.6. find the
following
(a) the mean of X
(b) the standard deviation of X
(c) P(X<4)
(d) P(X>5)
(e) P(3<X<6)

Let X denote a random variable that follows a binomial
distribution with parameters n=5, p=0.3, and Y denote a random
variable that has a Poisson distribution with parameter λ = 6.
Additionally, assume that X and Y are independent random
variables.
Derive the joint probability distribution function for X and Y.
Make sure to explain your steps.

Consider a random variable X with the following probability
distribution:
P(X=0) = 0.08, P(X=1) = 0.22,
P(X=2) = 0.25, P(X=3) = 0.25,
P(X=4) = 0.15, P(X=5) =
0.05
Find the expected value of X and the standard deviation of
X.

random variable x has a Normal distribution, N(75,25).
P(65<X<80) = ______________ .
Random variable Y has a Binomial Distribution, B(8, 0.5).
P(Y<5) = ______________ .
Let P(A)=0,6, P(B)=0.4, and P(A and B ) = 0.88, P(A and B) =
_____________ .
For events A,B, C, P(A)=0.2, P(B)=0.1, and P(C)=0.6, then what
is the range of P(A or B or C)? ___________ .

Let x be a discrete random variable with the following
probability distribution
x: -1 , 0 , 1, 2
P(x) 0.3 , 0.2 , 0.15 , 0.35
Find the mean and the standard deviation of x

1.
Determine whether the distribution represents a probability
distribution.
X
3
7
9
12
14
P(X)
4/13
1/13
3/13
1/13
2/13
2. Determine whether the distribution represents a probability
distribution.
X 5 7 9
P(X) 0.6 0.8 -0.4
3. Determine whether the distribution represents a probability
distribution.
X 20 30 40 50
P(X) 0.05 0.35 0.4 0.2

If X is a random variable with a probability distribution that
is given in the following table where a and b are unknown
constants.
X -1 0 a 3 b P(X = x) 0.1 0.15a 0.2 0.03b 0.4
(a) Find a and b such that E(5 + 100X) = 260.
(b) Find the variance of X.

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