3. Determine whether each of the distributions given below represents a probability distribution. Justify answer

a) x |1 | 2 | 3 | 4

P(x) |1/8| 1/8| 3/8 | 1/8

b) x | 20 | 30| 40 | 50

P(x)| 0.3|0.2| 0.1| 0.4

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- Jun 30th 2007, 01:14 PMharryprobability
3. Determine whether each of the distributions given below represents a probability distribution. Justify answer

a) x |1 | 2 | 3 | 4

P(x) |1/8| 1/8| 3/8 | 1/8

b) x | 20 | 30| 40 | 50

P(x)| 0.3|0.2| 0.1| 0.4 - Jun 30th 2007, 01:31 PMred_dog
The sum of probabilities must be equal to 1.

In the first "distribution" the sum is $\displaystyle \displaystyle \frac{6}{8}\neq 1$, so isn't a distribution.

In the second the sum is equal to 1, so it is a corect distribution. - Jun 30th 2007, 01:31 PMPlato
There are two requirements:

$\displaystyle 0 \le P(x) \le 1$ and $\displaystyle \sum\limits_x {P(x)} = 1$.

Now you check both of those for these properties.

EDIT: What is the point of simply handing out simple answers?

Is that what teaching has come to? - Jun 30th 2007, 01:35 PMSoroban
Hello, Harry!

Quote:

3. Determine whether each of the distributions given below represents a probability distribution.

$\displaystyle a)\;\;\begin{array}{cccccccccc}x & | & 1 & | & 2 & | & 3 & | & 4 & | \\ \hline

P(x) & | & \frac{1}{8} & | & \frac{1}{8} & | & \frac{3}{8} & | & \frac{1}{8} & | \end{array}$

Quote:

$\displaystyle b)\;\;\begin{array}{cccccccccc} x & | & 20 & | & 30 & | & 40 & | & 50 & | \\ \hline

P(x) & | & 0.3 & | & 0.2 & | & 0.1 & | & 0.4 & | \end{array}$

Yes . . . The probabilities are positive and add up to $\displaystyle 1$.