Random Variable Problems & Solutions

Give a counter example to the statement $E (X Y) = E (X) E (Y)$ implies
that X and Y are independent.

Emily-Jane Bray 2021-03-06

Are all infinite random variables necessary continuous?Explain.

FobelloE 2021-03-02

A population of values has a normal distribution with $μ = 226.7 and σ = 59.8$ . If a random sample size of n=24 is selected.
Find the probability that a single randomly selected value is greater than 192.5.

Tabansi 2021-03-02

CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 96 auto insurance policies.
Find the probability that a single randomly selected value is less than 969 dollars.
$P (x < 969) = P (x < 969) =$ ?

Write your answers as numbers accurate to 4 decimal places.

Tolnaio 2021-03-02

Let X and Y be Bernoulli random variables. Let $Z = X Y$ .
a) Show that Z is a Bernoulli random variable.
b) Show that if X and Y are independent, then $P_{Z} = P_{X} P_{Y}$ .

EunoR 2021-03-01

A population of values has a normal distribution with mean 191.4 and standard deviation of 69.7. A random sample of size $n = 153$ is drawn.
Find the probability that a sample of size $n = 153$ is randomly selected with a mean between 188 and 206.6. Round your answer to four decimal places.
P=?

Emily-Jane Bray 2021-02-26

Suppose that $X_{1}, X_{2}, . . ., X_{200}$ is a set of independent and identically distributed Gamma random variables with parameters $α = 4, λ = 3$ .
Describe the normal distribution that would correspond to the sum of those 200 random variables if the Central Limit Theorem holds.

Josalynn 2021-02-25

Provide the formula for mean all symbols.

Burhan Hopper 2021-02-25

Round each z-score to the nearest hundredth.
A data set has a mean of
$x = 6.8$
and a standard deviation of 2.5. Find the z-score.
$x = 7.2$

nicekikah 2021-02-25

Let $X \sim N (6, 4)$ .Find the probabilities $P (X > 8)$ .

aflacatn 2021-02-25

Assume that there is a sampling distribution of $\overset{―}{x}$ of size 34 and they are selected at random from a normally distributed with a mean of 45 and a standard deviation of 6.2.
Find the probability that 1 randomly selected person has a value less than 40.

emancipezN 2021-02-24

A normal population has mean $μ = 20$ and standard deviation $σ = 4$ .
What is the probability that a randomly chosen value will be greater than 25?

EunoR 2021-02-24

A normal distribution with $μ = 73.1$ and $σ = 28.1$ exists for a population of values. You want to select an $n = 131$ -piece random sample at random. Calculate the likelihood that a single value chosen at random is higher than 69.7
$P (X > 69.7) =$ ?

necessaryh 2021-02-21

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 192 had kids. Based on this, plot a $99 %$ confidence interval for the proportion of adult residents who are parents in a given county.
Express your answer in the form of three inequalities. Provide your responses in decimal fractions up to three places $< p <$ Express the same answer using a point estimate and a margin of error. Provide your responses as decimals, to three places.
$p = \pm$

mattgondek4 2021-02-21

A population of values has a normal distribution with $μ = 221.6$ and $σ = 44.1$ . You intend to draw a random sample of size $n = 42$ .
Find the probability that a single randomly selected value is between 221.6 and 229.1.
$P (221.6 < X < 229.1) =$ ?
Write your answers as numbers accurate to 4 decimal places.

avissidep 2021-02-19

Discrete or Continuous? II Identify the following as discrete or continuous random variables:
a.Number of overdue accounts in a department store at a particular time
b.Your blood pressure

waigaK 2021-02-19

A population of values has a normal distribution with $μ = 216.9$ and $σ = 87.1$ . You intend to draw a random sample of size $n = 97$ .
Find the probability that a single randomly selected value is between 193 and 244.3.
$P (193 < X < 244.3) =$ ?
Write your answers as numbers accurate to 4 decimal places.

sjeikdom0 2021-02-16

A population of values has a normal distribution with $μ = 182.5$ and $σ = 49.4$ . You intend to draw a random sample of size $n = 15$ .
Find the probability that a single randomly selected value is greater than 169.7.
$P (X > 169.7) =$ ?
Write your answers as numbers accurate to 4 decimal places.

midtlinjeg 2021-02-13

A population of values has a normal distribution with $μ = 192.6$ and $σ = 34.4$ . You intend to draw a random sample of size $n = 173$ .
Find the probability that a single randomly selected value is less than 186.1.
$P (X < 186.1) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Sinead Mcgee 2021-02-12

Discrete or Continuous? Identify the following as discrete or continuous random variables:
a. Total number of points scored in a football game
b. Shelf life of a particular drug
c. Height of the oceans

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