Random Variable Problems & Solutions

A distribution of values is normal with a mean of 79.5 and a standard deviation of 7.4.
Find the probability that a randomly selected value is between 71.4 and 78.
$P (71.4 < x < 78) = P (< z <) =$ ?

Trent Carpenter 2021-01-19

How can the sample covariance be used to estimate the covariance of random variables?

pedzenekO 2021-01-19

To know:Distribution of the sum of multinomial random variables.
Covariance of multinomial random variables,
$C O V (N_{i}, N_{j}) = - m P_{i} P_{j},$

a2linetagadaW 2021-01-19

A population of values has a normal distribution with $μ = 200.7$ and $σ = 10$ . You intend to draw a random sample of size $n = 178$
Find the probability that a sample of size $n = 178$ is randomly selected with a mean less than 198.6.
$P (M < 198.6) =$ ?

Dillard 2021-01-15

The random variable X follows a normal distribution $? (20, 102)$ .
Find $P (10 < ? < 35)$ ,

glamrockqueen7 2021-01-13

Explain the rules 3 and 4 in sum of several random variables.

mattgondek4 2021-01-10

A population of values has a normal distribution with mean =136.4 and standard deviation =30.2. A random sample of size $n = 158$ is drawn.
Find the probability that a single randomly selected value is greater than 135. Roung your answer to four decimal places.
$P (X > 135) =$ ?

nicekikah 2021-01-06

If X and Y are random variables and c is any constant, show that $E (c X) = c E (X)$ .

Line 2021-01-05

A population of values has a normal distribution with $μ = 99.6$ and $σ = 35.1$ . You intend to draw a random sample of size $n = 84$ .
Find the probability that a sample of size $n = 84$ is randomly selected with a mean between 98.5 and 100.7.
$P (98.5 < \overset{―}{X} < 100.7) =$ ?
Write your answers as numbers accurate to 4 decimal places.

SchachtN 2021-01-05

If X and Y are random variables and c is any constant, show that $E (X - Y) = E (X) - E (Y)$ .

Tobias Ali 2021-01-02

The amount of time, in minutes, for an airplane to obtain clearance for take off at a certain airport is a random variable Y=3X-2, where X has the density function
$f (x) = {\begin{cases} \frac{1}{4} e^{\frac{- x}{4}}, x > 0 \\ 0, else where \end{cases}$
Find the mean and variance of the random variable Y?

emancipezN 2020-12-30

Consider a set of 20 independent and identically distributed uniform random variables in the interval (0,1). What is the expected value and variance of the sum, S, of these random variables?
Select one:
a. $E (S) = 10$ , $V a r (S) = 1.66667$
b. $E (S) = 200$ , $V a r (S) = 16.6667$
c. $E (S) = 100$ , $V a r (S) = 200$
a. $E (S) = 10$ , $V a r (S) = 12$

glasskerfu 2020-12-30

Whether the statement is true or false. Rewrite it as a true statement if it is false.

coexpennan 2020-12-29

CNBC recently reported that the mean annual cost of auto insurance is $998. Assume the standard deviation is $298.
Find the probability that a single randomly selected value is less than $985.
$P (X < 985) =$ ?
Write your answers as numbers accurate to 4 decimal places.

tabita57i 2020-12-28

Meaning for F and M assumed as independent random variables in context.
F and M are independent random variables.
For F:
Mean,
$μ_{F} = 120$

avissidep 2020-12-22

A population of values has a normal distribution with $μ = 77$ and $σ = 32.2$ . You intend to draw a random sample of size $n = 15$
Find the probability that a sample of size $n = 15$ is randomly selected with a mean between 59.5 and 98.6. $P (59.5 < \overset{―}{X} < 98.6) =$ ?
Write your answers as numbers accurate to 4 decimal places.

ankarskogC 2020-12-15

A population of values has a normal distribution with $μ = 26.8$ and $σ = 33.8$ . You intend to draw a random sample of size $n = 89$ .
Find the probability that a sample of size $n = 89$ is randomly selected with a mean between 17.1 and 25.
$P (17.1 < M < 25) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Zoe Oneal 2020-12-13

For a population with a mean of $μ = 100$ and a standard deviation of $σ = 20$ ,
Find the X values.
$z = + 1.80$ .

chillywilly12a 2020-12-09

For a population with a mean of $μ = 100$ and a standard deviation of $σ = 20$ ,
Find the X values.
$z = - .40$ .

Tahmid Knox 2020-12-06

A population of values has a normal distribution with $μ = 13.7$ and $σ = 22$ .
You intend to draw a random sample of size $n = 78$ .
Find the probability that a single randomly selected value is less than 11.5.
$P (X < 11.5) =$ ?
Write your answers as numbers accurate to 4 decimal places.

When you have an equation that deals with random variables, always start with an explanation related to some random variable examples. It is what the majority of skilled engineers do because it is the only way how one can avoid mistakes when working with statistical data. Even though this part of statistics and probability may seem overly complex, approach every random variable equation through the lens of probability as you seek answers to your questions. Compare provided solutions, see similarities, and you will achieve the most efficient solutions.

Explore Random Variables: Examples & Equations