Unit 5: continuous random variables Flashcards
For continuous random variables, probabilities correspond to areas under the density curve
true
The area under any continuous probability distribution is 1.
true
A probability density function can take on negative values.
False
f(x) ≥ 0 everywhere.
A probability density function can take on values greater than 1
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
f(x) = P(X = x) for all x.
False
f(x)= height of the curve, the height of the curve is not a probability
f(x) = µ whenever the distribution is symmetric
false
The uniform distribution is symmetric.
true
For any uniform distribution, the mean and median are equal
true
For any uniform distribution, Q1 = −Q3.
false, only if the mean is 0
For any uniform distribution, Q3 − Q2 = Q2 − Q1.
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.
If a random variable has a uniform distribution, then it cannot take on negative values
false
If a random variable has a uniform distribution, then its standard deviation is greater than its
mean.
false
Depending on the value of the parameters, the standard deviation can be greater
than, less than, or equal to the mean.
The normal distribution is symmetric about µ
true
If X is a normally distributed random variable, then P(X < 0) > 0.
True. A normally
distributed random variable can take on any finite value.
If X is a normally distributed random variable, then P(X = 0) = 0
True.
The probability a
continuous random variable takes on any single value is always 0
The standard deviation of a normal distribution cannot be greater than the mean
false
The mean and median of a normal distribution are always equal.
True. The normal distribution
is symmetric, and the mean and median are equal in symmetric distributions.
If X has a normal distribution with mean µ and standard deviation σ, then X−µ/σ
has the standard normal distribution.
true
If Z has the standard normal distribution, then the mean and standard deviation of Z are equal.
false, mean would =0 and STD =1
The first quartile of the standard normal distribution is greater than 0.
False. The first quartile
is approximately −0.67
The first quartile of any normal distribution is greater than 0.
False. Any of the percentiles can
be negative, depending on the parameters of the distribution
If X has a normal distribution, then P(X > µ) = P(X < µ).
True. Since the normal
distribution is symmetric about µ,
