X=Number of Heads 3 2 1 0 Probability P(X) 34.3% 44.1% 18.9% 2.7% 1. A certain unfair coin will be tossed three times in a row. A random variable X will be used to record the total number of heads received out of the three tosses. The discrete probability model for this random variable X is represented in the small table shown here. In this discrete probability model: What is the Expected Value of X ?
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!
| X=Number of Heads | 3 | 2 | 1 | 0 |
| Probability P(X) | 34.3% | 44.1% | 18.9% | 2.7% |
1.
A certain unfair coin will be tossed three times in a row.
A random variable X will be used to record the total number of heads received out of the three tosses.
The discrete probability model for this random variable X is represented in the small table shown here.
In this discrete probability model: What is the
Show one digit past the decimal point, and state just the number part of your answer (no units).
In this discrete probability model: What is the Variance for X ?
Show two digits past the decimal point.
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Hint:
- Remember to show just a number for each answer (no units)
- Remember to show each answer as just a decimal number (not a percentage value)
- Remember to show the correct number of digits past the decimal point as requested in each separate problem
- Remember there are examples for each of these calculations, demonstrated in an instructional video for our course
2.
A certain unfair coin will be tossed three times in a row.
A random variable X will be used to record the total number of heads received out of the three tosses.
The discrete probability model for this random variable X is represented in the small table shown here.
In this discrete probability model: What is the Standard Deviation of X ?
Show four digits past the decimal point, and state just the number part of your answer (no units).
In this discrete probability model: What is P(X>1) ?
Write your answer as a percentage value, showing one digit past the decimal point.
Include a percentage symbol after your answer (no spaces).
In this discrete probability model: What is P(X≤1) ?
Write your answer as a percentage value, showing one digit past the decimal point.
Include a percentage symbol after your answer (no spaces).
In this discrete probability model: What is P(X≠1) ?
Write your answer as a percentage value, showing one digit past the decimal point.
Include a percentage symbol after your answer (no spaces).
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