Points:
The question is incomplete as the value of x is not given and what is required is not stated.
<em>However, I'll assume that x = 5</em>
Going by the details of the question, possible questions could be:
- Expected number of hits
- Variance and Standard Deviation of hits
Answer:
See Explanation
Step-by-step explanation:
Given
Represent the probability with p.
So:
![p = 0.8](https://tex.z-dn.net/?f=p%20%3D%200.8)
Solving (a): The expected number of hits.
In probability, the expected number is calculated as:
![E(x) = p * x](https://tex.z-dn.net/?f=E%28x%29%20%3D%20p%20%2A%20x)
Substitute values for p and x
![E(x) = 0.8 * 5](https://tex.z-dn.net/?f=E%28x%29%20%3D%200.8%20%2A%205)
<em>Remember that 5 is an assumed value of x</em>
![E(x) = 4](https://tex.z-dn.net/?f=E%28x%29%20%3D%204)
<em>Hence, the expected number of hits when 5 missiles is fired is 4</em>
Solving (b): Variance
In probability, variance is calculated as:
![variance = x*p*(1-p)](https://tex.z-dn.net/?f=variance%20%3D%20x%2Ap%2A%281-p%29)
Substitute values for p and x
![variance = 5*0.8*(1-0.8)](https://tex.z-dn.net/?f=variance%20%3D%205%2A0.8%2A%281-0.8%29)
![variance = 5*0.8*0.2](https://tex.z-dn.net/?f=variance%20%3D%205%2A0.8%2A0.2)
![variance = 0.8](https://tex.z-dn.net/?f=variance%20%3D%200.8)
<em>Hence, the variance is 0.8</em>
Solving (c): The standard deviation
In probability, the standard deviation is calculated as:
![SD= \sqrt{Variance](https://tex.z-dn.net/?f=SD%3D%20%5Csqrt%7BVariance)
Substitute values for variance
![SD= \sqrt{0.8](https://tex.z-dn.net/?f=SD%3D%20%5Csqrt%7B0.8)
![SD= 0.89](https://tex.z-dn.net/?f=SD%3D%200.89)
<em>Hence, the standard deviation is 0.89</em>