mathisaqeosmw
23.03.2020 •
Mathematics
2. A random test score X is obtained from a class with students who fall into two groups. For the first group X is conditionally Gaussian with mean 80 and variance 20, while for the second group X is conditionally Gaussian with mean 20 and variance 10. The probability that a student is in the first group is 0.6. (a) Find E [X] and Var [X] . (b) Assuming the grades are assigned as in the notes, find the probability that a randomly selected exam gets an A, B, C,D or F grade (in terms of the Φ function
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Ответ:
E (X) = 56 and V (X) = 880.
Step-by-step explanation:
The random variable X denotes the test scores obtained from a class with students who fall into two groups.
Let's denote the test scores of first group as X₁ and the test scores of second group as X₂.
The information provided is:
The probability of selecting a student from the first group is, p = 0.60.
Then the probability of selecting a student from the second group is,
q = 1 - p = 1 - 0.60 = 0.40.
(a)
Compute the expected test score obtained as follows:
E (X) = p × E (X₁) + q × E (X₂)
Thus, the expected test score obtained is E (X) = 56.
Compute the value of E (X₁²) as follows:
Compute the value of E (X₂²) as follows:
Compute the value of E (X²) as follows:
Compute the variance of the test scores obtained as follows:
Thus, the variance of the test scores obtained is, V(X) = 880.
(b)
Since the division of grades is not provided, i.e. which score is assigned what grade we cannot compute the probability of randomly selecting an exam with grade A, B, C, D or F.
Ответ:
x=11
Step-by-step explanation:
And you didnt give the equation for FDE but substitute 11 in for X