The table below shows the probability distribution function of the number of accidents (X) occur in a day by taxis belonging to a taxi company. x 0 1 2 3 4 P(X = x) 0.5 0.15 0.05 2k k (a) Find the value of k. (b) Find the expected value and standard deviation of the number of a
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!
The table below shows the
| x | 0 | 1 | 2 | 3 | 4 |
| P(X = x) | 0.5 | 0.15 | 0.05 | 2k | k |
(a) Find the value of k.
(b) Find the
(c) Assume the net profit ($), Y, of the taxi company in a day is given by Y = 10000 – 4000X. Find the
expected value, variance, and standard deviation of the net profit of the taxi company in a day.
(d) What is the maximum profit the company earn in a day? What is the corresponding probability?
(e) What is the probability that the company loses money in a day?
(f) Find the probability that there are exactly 3 days that the company loses money in a week (7 days).
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