Data
6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,8
Answer:
(a) shown in the attachment
(b) 0.54
(c) 5.32
<h2>Step-by-step explanation:</h2>(a) The frequency distribution table has been added to this response.
The table contains four columns:
<em>First column (x)</em>: The discrete values of the marks
<em>Second column (f)</em>: The corresponding frequency of the marks
<em>Third column (d)</em> : The difference between each mark(x) and the assumed mean(A). i.e d = x - A (Where A = 6 from the question)
<em>Fourth column (fd)</em>: The product of the first column and the third column. i.e f * d
(b) From the table, it can be deduced that the modal score is 6
This is because the score 6 has the highest number of frequency which is <em>6</em>
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(c) If a student is selected at random, the probability P(>5), that the student scored more than 5 is given as follows;
P( >5 ) = [The sum of frequencies of marks greater than 5] / [Total frequency]
P( >5 ) = [6 + 4 + 2 + 3 + 1] / [28]
P( >5 ) = 15 / 28 = 0.54
Therefore, the probability that the student scored more than 5 is 0.54
(d) To get the arithmetic mean, M, from the assumed mean A = 6, we use the following relation;
M = A + [∑fd / N] -----------(*)
Where
N = total frequency = 28
A = 6
∑fd = sum of the items on the fourth column = -19
Substitute these values into equation (*)
M = 6 + [-19 / 28]
M = 149 / 28
M = 5.32
Therefore, the arithmetic mean is 5.32
Answer:
Step-by-step explanation:
The given differential equation is:
the main task here is to determine the singular points of the given differential equation and Classify each singular point as regular or irregular.
So, for a regular singular point ; is located at the first power in the denominator of P(x) likewise at the Q(x) in the second power of the denominator. If that is not the case, then it is termed as an irregular singular point.
Let first convert it to standard form by dividing through with x³
The standard form of the differential equation is :
Thus;
The zeros of is 0
Therefore , the singular points of above given differential equation is 0
Classify each singular point as regular or irregular.
Let p(x) = xP(x) and q(x) = x²Q(x)
p(x) = xP(x)
p(x) =
p(x) = 2
q(x) = x²Q(x)
q(x) =
q(x) =
The function (f) is analytic if at a given point a it is represented by power series in x-a either with a positive or infinite radius of convergence.
Thus ; from above; we can say that q(x) is not analytic at x = 0
do not satisfy the condition,at most to the second power in the denominator of Q(x).
Thus, the point x =0 is an irregular singular point