39 results for "expectation".
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Question in Odds and Ends
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Question in MXB241 Weekly Quizzes
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Question in MXB241 Weekly Quizzes
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Question in MXB241 Weekly Quizzes
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Question in MXB241 Weekly Quizzes
No description given
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Question in Content created by Newcastle University
A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.
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Question in Content created by Newcastle University
Application of the Poisson distribution given expected number of events per interval.
Finding probabilities using the Poisson distribution.
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Question in Content created by Newcastle University
Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.
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Question in Bill's workspace
Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.
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Question in Bill's workspace
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 Content created by Newcastle University
Using a random sample from a population with given mean and variance, find the expectation and variance of three estimators of $\mu$. Unbiased, efficient?
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Question in Content created by Newcastle University
Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$.
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Question in Content created by Newcastle University
Exercise using a given uniform distribution $Y$, calculating the expectation and variance as well as asking for the CDF. Also finding $P( b \lt Y \lt c)$ for given values of $b,\;c$.
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Question in Content created by Newcastle University
The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.
Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.
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Question in Content created by Newcastle University
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 Content created by Newcastle University
Given three linear combinations of four i.i.d. variables, find the expectation and variance of these estimators of the mean $\mu$. Which are unbiased and efficient?
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Question in Content created by Newcastle University
Exercise using a given uniform distribution $Y$, calculating the expectation and variance as well as asking for the CDF. Also finding $P(Y \le a)$ and $P( b \lt Y \lt c)$ for a given values $a,\;b,\;c$.
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Question in Content created by Newcastle University
Given a piecewise CDF $F_X(b)$ which is discontinuous at several points, find the probabilities at those points and also find the value of $F_X(b)$ at a continuous point and the expectation.
This cdf is a step function and is therefore the cdf of a discrete random variable. This should be stated somewhere in the statement or the solution. Apart from this the question is correct.
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Question in Content created by Newcastle University
Given the PDF for $Y \sim \operatorname{Exp}(\lambda)$ find the CDF, $P(a \le Y \le b)$ and $\operatorname{E}[Y],\;\operatorname{Var}(Y)$
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Question in Content created by Newcastle University
Application of the Poisson distribution given expected number of events per interval.
Finding probabilities using the Poisson distribution.
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Question in Content created by Newcastle University
Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.
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Question in Content created by Newcastle University
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 Content created by Newcastle University
Application of the binomial distribution given probabilities of success of an event.
Finding probabilities using the binomial distribution.
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Question in Statistics
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 Statistics
Exercise using a given uniform distribution $X$, calculating the expectation and variance. Also finding $P(X \le a)$ for a given value $a$.
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Question in Statistics
A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$.
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Question in Statistics
Application of the binomial distribution given probabilities of success of an event.
Finding probabilities using the binomial distribution.
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Question in Brad's workspace
Application of the Poisson distribution given expected number of events per interval.
Finding probabilities using the Poisson distribution.
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Question in Rachel's workspace
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
The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.
Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.