By letting
we get derivatives
a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to
Examine the lowest degree term , which gives rise to the indicial equation,
with roots at r = 0 and r = 4/5.
b) The recurrence for the coefficients is
so that with r = 4/5, the coefficients are governed by
c) Starting with , we find
so that the first three terms of the solution are
Answer:
The teacher should set the score 7 as the lowest passing grade.
Step-by-step explanation:
Let <em>X</em> = number of correct guesses.
All the questions are of true-false format.
The probability of getting a correct answer is, <em>p</em> = 0.50.
The total number of questions is, <em>n</em> = 10.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 10 and <em>p </em>= 0.50.
The probability mass function of <em>X</em> is:
Now the teaches chose the grading scheme such that the probability of passing a student who guesses on every question is less than 0.05.
Then the probability of failing such a students is at least 1 - 0.05 = 0.95.
Compute the probability distribution of <em>X</em>.
Consider the probability distribution attached below.
The value of <em>x</em> for which P (X ≤ x) is at least 0.95 is, <em>x</em> = 7.
So the teacher should set the score 7 as the lowest passing grade.
