A true-false test consists of 20 questions, each of which has one correct answer: true, or false. One point is awarded for every correct answer, but one point is taken off for each wrong answer. Suppose a student answers every question by guessing at random, independently of other questions. Let S be the student¢s score on the test.Find E(S), SE(S), P(S=0)

Question

A true-false test consists of 20 questions, each of which has one correct answer: true, or false. One point is awarded for every correct answer, but one point is taken off for each wrong answer. Suppose a student answers every question by guessing at random, independently of other questions. Let S be the student¢s score on the test.Find E(S), SE(S), P(S=0)

Answer 1

E(S)= 0

Anyone for SE(S) and P(S=0) ?

Answer 2

Thanks FLu!

Anyone for SE(S) and P(S=0)?

Answer 3

Thanks from me Flu

Answer 4

Thanks, anyone for the rest?

Answer 5

Could anyone tell me the SE(S)?

Answer 6

SE(E)- 4.472

Answer 7

Thanks Pebble.

Answer 8

Thanks Pebble, did someone solves or find the C....... P(S=0)?

Answer 9

To calculate the expected value of the student's score (E(S)), we need to determine the probability of each possible score and multiply it by that score. In this case, there are 20 questions, and each question has two possible answers (true or false). Therefore, the total number of possible ways the student can answer the test is 2^20.

To calculate the probability of each score, we can use the binomial probability formula:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where:
- P(X=k) is the probability of getting exactly k correct answers
- C(n, k) is the number of combinations of n items taken k at a time (in this case, n is the total number of questions, and k is the number of correct answers)
- p is the probability of getting a single question correct (0.5 in this case since there are two equally likely options)
- n is the total number of questions

Let's calculate the expected value (E(S)).

First, let's calculate the probability of getting each possible number of correct answers:

P(X=0) = C(20, 0) * (0.5)^0 * (1-0.5)^20 = 1 * 1 * 0.5^20 ≈ 0.0000009537
P(X=1) = C(20, 1) * (0.5)^1 * (1-0.5)^19 = 20 * 0.5 * 0.5^19 ≈ 0.0000190735
P(X=2) = C(20, 2) * (0.5)^2 * (1-0.5)^18 = 190 * 0.25 * 0.5^18 ≈ 0.000190735
...

Calculating the probability for each possible score, we get:

P(X=0) ≈ 0.0000009537
P(X=1) ≈ 0.0000190735
P(X=2) ≈ 0.000190735
P(X=3) ≈ 0.0011444107
...
P(X=19) ≈ 0.000190735
P(X=20) ≈ 0.0000009537

Now, let's calculate the expected value (E(S)):

E(S) = 0 * P(X=0) + 1 * P(X=1) + 2 * P(X=2) + 3 * P(X=3) + ... + 20 * P(X=20)

E(S) ≈ 0 * 0.0000009537 + 1 * 0.0000190735 + 2 * 0.000190735 + 3 * 0.0011444107 + ... + 20 * 0.0000009537

Calculate the sum of these terms to get the expected value.

Next, to calculate the standard error (SE(S)), we can use the formula:

SE(S) = sqrt[ Σ{ [X − E(S)]^2 * P(X) } ]

Where Σ represents the sum from X=0 to X=20.

Finally, to calculate the probability of the student getting a score of 0 (P(S=0)), we can simply use the P(X=0) value calculated earlier.

P(S=0) ≈ 0.0000009537

By following these steps and performing the calculations, you should be able to determine E(S), SE(S), and P(S=0) for the given scenario.