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Based on past experience, it is assumed that the number of flaws of per metre in rolls of wrapping paper follows a Poisson distribution with a mean of 2 flaws per 4 metres of paper. The probability (correct to 2 decimal places) that more than 2 flaws will be observed in 5 metres of wrapping paper produced is:
A random sample of 11 observations was taken from normal population. The sample mean and
standard deviation are 74.5 and 9 accordingly. Can we infer at 5% significance level that the
population mean is greater than 70?
5. Repeat number 4 with assuming the population standard deviation = 9
In a survey conducted among a random sample of students the following observations were made regarding their gender and learning environment preferences during the COVID-19 pandemic:
168 prefer online learning
202 prefer face to face learning
180 prefer blended learning
34 male students prefer online learning and
70 male students prefer blended learning
106 female students prefer face to face learning
Required:
a) What is the probability that a female student is chosen?
b) What is the probability that a male student prefers face to face learning?
c) What is the probability that a student prefers online or blended learning?
d) If it’s known that the student is female, what is the probability that this student prefers online learning.
e) Using a practical example, explain the difference between mutually exclusive events and independent events.
Consider a linear mapping f : V→W with dim V = n and dim W = m. Prove that
i) Nullity(f) = 0 if f is one-to-one
ii) f is onto if R(f) = m
Let T: P2→P2 be the mapping defined by
T(a0 + a1x + a2x2) = 3a0 + a1x + (a0 + a1)x2
i) Show that T is linear
ii) Find a basis for the kernel of T
iii) Find a basis for the range of T
An element with mass 290 grams decays by 13.2% per minute. How much of the element is remaining after 14 minutes, the nearest of a gram?
By examining the determinant of the coefficient matrix, show that the following system has a nontrivial solution if and only if α = β
x + y + αz = 0
x + y + βz = 0
αx + βy + z = 0
If the characteristic polynomial of a matrix A is p(λ) = λ2+ 1, then A is invertible
An n x n matrix with fewer than n distinct eigen values is not diagonalizable
The following are the loss amount in thousands of dollars from three portfolio of insurance policies
Portfolio Y1: 43 30 27 24
Portfolio Y2: 43 30 27 24
Portfolio Y3: 43 30 27 24
Portfolio Y4: 43 30 27 24
Determine
i) The mean vectors of the portfolios
ii)Variance covariance matrix of the portfolios
iii) Correlation matrix of the portfolios
#339914 on Dec 2023