(a) Construct a binomial probability distribution with the given parameters. (b) Compute the mean and standard deviation of the random variable. n=5, p=0.25 (a) To construct a binomial probability distribution, complete the table to the right. P(x) 3 4 (Round to four decimal places as needed.) (b) H, = (Round to the nearest hundredth as needed.) (Round to the nearest tenth as needed.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Let X be the binomial random variable with parameters n = 5, p = 0.25.
The probability mass function of X is given by;
(a) Hence the binomial probability distribution table is;
| x | P(x) |
| 0 | 0.2373 |
| 1 | 0.3955 |
| 2 | 0.2637 |
| 3 | 0.0879 |
| 4 | 0.0146 |
| 5 | 0.0010 |
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