317 results authored by Simon Thomas - search across all users.
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Question in Trigonometry
Using trig identities to find solutions to equations
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Question in Matrices
Elementary Exercises in multiplying matrices.
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Question in Matrices
Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector (x=1).
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Question in Stats
The random variable X has a PDF which involves a parameter c. Find the value of c. Find the distribution function FX(x) and P(a<X<b).
Also find the expectation E[X]=∫∞−∞xfX(x)dx.
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Question in Calculus
Finding the coordinates and determining the nature of the stationary points on a polynomial function
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Question in Basic vectors
Find the dot product and the angle between two vectors
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Question in Basic vectors
Given vectors \boldsymbol{a,\;b}, find \boldsymbol{a\times b}
rebelmaths
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Question in Differential Equations
Find the solution of a constant coefficient second order ordinary differential equation of the form ay''+by'+cy=0.
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Question in Matrices
Find the determinant and inverse of three 2 \times 2 invertible matrices.
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Question in Matrices
Cofactors Determinant and inverse of a 3x3 matrix.
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Question in Stats
Application of the Poisson distribution given expected number of events per interval.
Finding probabilities using the Poisson distribution.
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Question in Stats
Given a random variable X normally distributed as \operatorname{N}(m,\sigma^2) find probabilities P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m.
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Question in Stats
Application of the binomial distribution given probabilities of success of an event.
Finding probabilities using the binomial distribution.
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Question in Stats
Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised.
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Question in Stats
Normal distribution X \sim N(\mu,\sigma^2) given. Find P(a \lt X \lt b). Find expectation, variance, P(c \lt \overline{X} \lt d) for sample mean \overline{X}.
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Question in Stats
Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis.
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Question in Stats
Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.