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

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.

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!

the answer is 489

step-by-step explanation: