True/False — Uniform, PDF/CDF, and Binomial concepts.
1) A PDF describes probabilities at single points for discrete variables.
2) A CDF always increases or stays flat as x increases.
3) For a continuous uniform [a,b], the PDF is constant at height 1/(b+a).
4) A fair die is an example of a discrete uniform distribution.
5) For a fair die, the mean outcome is 3.0.
6) The variance measures the center of the distribution.
7) The variance of a distribution describes the spread around the mean.
8) Binomial(n,p) models the number of successes in n independent trials.
9) Binomial(10,0.5) models flipping a fair coin 10 times and counting heads.
10) The mean of Binomial(n,p) is the expected number of successes, np.
11) The variance of Binomial(n,p) is always larger than the mean.
12) For Binomial(20,0.1), the expected number of successes is 2.
13) The CDF at x gives the probability that the random variable is greater than x.
14) In a continuous uniform [0,1], the probability that X is between 0.2 and 0.5 is 0.25.
15) In a discrete uniform {1,…,10}, the variance is (10²−1)/12 = 99/12.