Part 1 The random variable X represents the number of cars per household in a town of 1000 households along with the corresponding probabilities. X 0 1 2 3 4 Probability of X 0.125 0.428 0.256 0.108 0.083 a. Verify that probability distribution for the random variable X is valid. b. Calculate the expected value of X. c. What is the probability that X<2?
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!
Part 1
The random variable X represents the number of cars per household in a town of 1000 households along with the corresponding probabilities.
| X | 0 | 1 | 2 | 3 | 4 |
| 0.125 | 0.428 | 0.256 | 0.108 | 0.083 |
a. Verify that probability distribution for the random variable X is valid.
b. Calculate the
c. What is the probability that X<2?
Part 2
a. Calculate the mean and standard deviation of the sampling distribution of x¯, the sample mean number of points scored by students for samples of size n=6.
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