Expected Value 56D575
1. The problem provides a table with number positions and their corresponding probabilities:
| संख्या स्थान (Number Position) | 7 | 9 | 8 | 10 |
|-------------------------------|---|---|---|----|
| संभावना (Probability) | 0 | 1 | 8 | 8 |
2. We are given $p=0.4$, but the problem does not specify what to calculate. Assuming we want to find the expected value (mean) of the distribution.
3. The expected value $E(X)$ is calculated by the formula:
$$E(X) = \sum (x_i \times p_i)$$
where $x_i$ are the number positions and $p_i$ are the probabilities.
4. First, normalize the probabilities since they do not sum to 1:
Sum of given probabilities = $0 + 1 + 8 + 8 = 17$
Normalized probabilities:
$$p_7 = \frac{0}{17} = 0$$
$$p_9 = \frac{1}{17}$$
$$p_8 = \frac{8}{17}$$
$$p_{10} = \frac{8}{17}$$
5. Calculate the expected value:
$$E(X) = 7 \times 0 + 9 \times \frac{1}{17} + 8 \times \frac{8}{17} + 10 \times \frac{8}{17}$$
$$= 0 + \frac{9}{17} + \frac{64}{17} + \frac{80}{17}$$
$$= \frac{9 + 64 + 80}{17} = \frac{153}{17} = 9$$
6. Therefore, the expected value of the distribution is $9$.
Note: If the problem requires a different calculation, please specify.