Probability Distributions

Which of the following could be the set of all possible outcomes for a random variable that follows a binomial distribution?

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11). -a basic property of binomial outcomes. They take on whole number values that must start at zero up to the upper limit n. The upper limit in this case is 11.

For a continuous distribution, P(a ≤ X ≤b) equals

= F(b) − F(a).

The lower limit of a normal distribution is

By definition, a true normal distribution has a positive probability density function from negative to positive infinity.

a continuous uniform distribution is calculated as follows:

F(X) = (X - a) / (b - a), where a and b are the upper and lower endpoints, respectively

what percent of the normal curve probability is more than two standard deviations from the mean

Five percent

the Binomial Random variable probability formula is:

P(x)=(nCx)*(p^x)*(1-p)^n-x

what percentage of the area under the normal curve falls between the mean and 1 standard deviation above the mean.

Sixty-eight percent

If a smooth curve is to represent a probability density function, what two requirements must be satisfied?

The area under the curve must be one and the curve must not fall below the horizontal axis.

Which of the following random variables would be most likely to follow a discrete uniform distribution

The outcome of a roll of a standard, six-sided die where X equals the number facing up on the die.

The binomial probability distribution is an example of

a discrete probability distribution

A binomial distribution counts the number of successes that occur in

a fixed number of independent trials that have mutually exclusive (i.e. yes or no) outcomes.

The probability density function of a continuous uniform distribution is best described by a

a horizontal line segment over a range of values such that the area under the segment (total probability of an outcome in the range) equals one.

A probability distribution must include

a listing of all the possible outcomes of an experiment and sum up to one.

sampling error is the difference between

a sample statistic and a population parameter is sampling error.

A continuous uniform distribution has both

an upper and a lower limit.

A discrete random variable is a variable that can

assume only certain clearly separated values resulting from a count of some set of items.

A random variable that has a countable number of possible values is called a:

discrete random variable

Because a cumulative probability function defines the probability that a random variable takes a value equal to or less than a given number,

for successively larger numbers, the cumulative probability values must stay the same or increase.

By definition, a normal distribution is completely described by its mean and variance.

mean and variance.

The expected value of a binomial distribution is

n × p. the expected value does not have to be a whole number:

A discrete random variable is one for which the

number of possible outcomes are countable, and for each possible outcome, there is a measurable and positive probability.

In a binomial distribution each observation has

only two possible outcomes that are mutually exclusive.

A discrete uniform random variable has equal

probabilities for each outcome.

a probability function

specifies the probability that the random variable takes on a specific value.

Binomial probability distributions give the result of a single outcome and are used to

study discrete random variables where you want to know the probability that an exact event will happen.

The number of advancing stocks in the DJIA in a day, is considered a discrete variable because

the DJIA consists of only 30 stocks, the answer associated with it would be a discrete random variable. -Random variables measuring time, rates of return and weight will be continuous.

A cumulative distribution function (cdf) gives the probability of an outcome for a random variable less than or equal to a specific value. For the random variable X, the cdf for the outcome 10 is 0.25.

which means there is a 25% probability that X will take a value less than or equal to 10.

The skewness of a normal distribution is

zero

In a continuous probability density function, the probability that any single value of a random variable occurs is equal to what?

zero. Since there are infinite potential outcomes in a continuous pdf, the probability of any single value of a random variable occurring is 1/infinity = 0.