Answer:
a) Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:
1) Independence between the trials (satisfied)
2) A value of n fixed , for this case is 20 (satisfied)
3) Probability of success p =0.2 fixed (Satisfied)
So then we have all the conditions and we can assume that:
b)
c)
d)
e)
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Part a
Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:
1) Independence between the trials (satisfied)
2) A value of n fixed , for this case is 20 (satisfied)
3) Probability of success p =0.2 fixed (Satisfied)
So then we have all the conditions and we can assume that:
Part b
Part c
For this case we just need to replace into the mass function and we got:
Part d
For this case we want this probability:
And we can solve this using the complement rule:
Part e
The expected value is given by: