Question

consider a probability distribution for the random variable x, where the mean is 1 and the standard deviation is 1. now consider the probability distribution y where y= 5x+4.

a). what is the mean of the probability distribution y?

b). what is the standard deviation of the probability distribution y?

round up to 0 decimal both.

Answer #1

In the following probability distribution, the random variable
x represents the number of activities a parent of a
6th to 8th-grade student is involved in. Complete parts (a)
through (f) below.
x
0
1
2
3
4
P(x)
0.395
0.075
0.199
0.195
0.136
(a) Verify that this is a discrete probability
distribution.
This is a discrete probability distribution because the sum of
the probabilities is ___and each probability is ___ (Less than or
equal to 1; Greater than or equal...

The probability distribution of a random variable X is
given.
x
−4
−2
0
2
4
p(X =
x)
0.2
0.1
0.3
0.2
0.2
Compute the mean, variance, and standard deviation of
X. (Round your answers to two decimal places.)
Find mean, variance, and standard deviation

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...

1. A random variable X has a normal distribution with a mean of
75 and a variance of 9. Calculate P(60 < X < 70.5). Round
your answer to 4 decimal places.
2. A random variable X has a uniform distribution with a minimum
of -50 and a maximum of -20. Calculate P(X > -25). Round your
answer to 4 decimal places.
3.Which of the following statements about continuous random
variables and continuous probability distributions is/are TRUE?
I. The probability...

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.

Given a random variable X following normal distribution with
mean of -3 and standard deviation of 4. Then random variable
Y=0.4X+5 is also normal.
(1)Find the distribution of Y, i.e. μy,σy
(2)Find the probabilities P(−4<X<0),P(−1<Y<0)
(3)Find the probabilities(let n size =8)
P(−4<X¯<0),P(3<Y¯<4)
(4)Find the 53th percentile of the distribution of X

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

Suppose that a random variable X has the distribution (pdf) f(x)
=kx(1 -x^2) for
0 < x < 1 and zero elsewhere.
a. Find k.
b. Find P(X >0. 8)
c. Find the mean of X.
d. Find the standard deviation of X.
2. Assume that test scores for all students on a statistics test
are normally
distributed with mean 82 and standard deviation 7.
a. Find the probability that a single student scores greater than
80.
b. Find the...

In the probability distribution to the right, the random
variable X represents the number of marriages an individual aged 15
years or older has been involved in. Compute the standard deviation
of the random variable X.
x
P(x)
0
0.264
1
0.583
2
0.119
3
0.028
4
0.005
5
0.001
=_______marriages
(Round to one decimal place as needed.)

Find the mean, variance, and standard deviation of the random
variable having the probability distribution given in the following
table. (Round your answers to four decimal places.)
Random variable, x
-7
-6
-5
-4
-3
P(X = x)
0.13
0.16
0.4
0.15
0.16

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