# probability

• Jun 30th 2007, 02:14 PM
harry
probability
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, 02:31 PM
red_dog
The sum of probabilities must be equal to 1.
In the first "distribution" the sum is $\displaystyle \frac{6}{8}\neq 1$, so isn't a distribution.
In the second the sum is equal to 1, so it is a corect distribution.
• Jun 30th 2007, 02:31 PM
Plato
There are two requirements:
$0 \le P(x) \le 1$ and $\sum\limits_x {P(x)} = 1$.

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, 02:35 PM
Soroban
Hello, Harry!

Quote:

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

$a)\;\;\begin{array}{cccccccccc}x & | & 1 & | & 2 & | & 3 & | & 4 & | \\ \hline
P(x) & | & \frac{1}{8} & | & \frac{1}{8} & | & \frac{3}{8} & | & \frac{1}{8} & | \end{array}$

No . . . The probabilities do not add up to $1$.

Quote:

$b)\;\;\begin{array}{cccccccccc} x & | & 20 & | & 30 & | & 40 & | & 50 & | \\ \hline
P(x) & | & 0.3 & | & 0.2 & | & 0.1 & | & 0.4 & | \end{array}$

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