Unit 5: continuous random variables

Question 1

For continuous random variables, probabilities correspond to areas under the density curve

Answer 1

true

Question 2

The area under any continuous probability distribution is 1.

Answer 2

true

Question 3

A probability density function can take on negative values.

Answer 3

False

f(x) ≥ 0 everywhere.

Question 4

A probability density function can take on values greater than 1

Answer 4

True.
The area under the
entire curve is 1, but the height of the curve can be greater than 1
**probabilty density function is f(x) the y axis

Question 5

f(x) = P(X = x) for all x.

Answer 5

False

f(x)= height of the curve, the height of the curve is not a probability

Question 6

f(x) = µ whenever the distribution is symmetric

Answer 6

false

Question 7

The uniform distribution is symmetric.

Answer 7

true

Question 8

For any uniform distribution, the mean and median are equal

Answer 8

true

Question 9

For any uniform distribution, Q1 = −Q3.

Answer 9

false, only if the mean is 0

Question 10

For any uniform distribution, Q3 − Q2 = Q2 − Q1.

Answer 10

true
For symmetric distributions, the
distance between the median and third quartile will be the same as the distance between the
median and first quartile.

Question 11

If a random variable has a uniform distribution, then it cannot take on negative values

Answer 11

false

Question 12

If a random variable has a uniform distribution, then its standard deviation is greater than its
mean.

Answer 12

false
Depending on the value of the parameters, the standard deviation can be greater
than, less than, or equal to the mean.

Question 13

The normal distribution is symmetric about µ

Answer 13

true

Question 14

If X is a normally distributed random variable, then P(X < 0) > 0.

Answer 14

True. A normally

distributed random variable can take on any finite value.

Question 15

If X is a normally distributed random variable, then P(X = 0) = 0

Answer 15

True.
The probability a
continuous random variable takes on any single value is always 0

Question 16

The standard deviation of a normal distribution cannot be greater than the mean

Answer 16

false

Question 17

The mean and median of a normal distribution are always equal.

Answer 17

True. The normal distribution

is symmetric, and the mean and median are equal in symmetric distributions.

Question 18

If X has a normal distribution with mean µ and standard deviation σ, then X−µ/σ
has the standard normal distribution.

Answer 18

true

Question 19

If Z has the standard normal distribution, then the mean and standard deviation of Z are equal.

Answer 19

false, mean would =0 and STD =1

Question 20

The first quartile of the standard normal distribution is greater than 0.

Answer 20

False. The first quartile

is approximately −0.67

Question 21

The first quartile of any normal distribution is greater than 0.

Answer 21

False. Any of the percentiles can

be negative, depending on the parameters of the distribution

Question 22

If X has a normal distribution, then P(X > µ) = P(X < µ).

Answer 22

True. Since the normal

distribution is symmetric about µ,