Mathematics, 16.12.2019 19:31, nerdypineapple
Let x be the total number of individuals of an endangered lizard species that are observed in a region on a given day. this observed number is assumed to be distributed according to a poisson distribution with a mean of 3 lizards. the endangered lizards can belong to either of two sub-species: graham or opalinus. let y be the number of graham lizards observed during this study (note that the total observed number of any lizard is denoted by x, so the observed number of opalinus lizards is given by x − y). it is known that graham lizards are by far the most common. in particular, the conditional distribution of the number of graham lizards (y) given the total number of all lizards (x) is binomial with parameters n = x and p = 0.8.
(a) write down the joint probability mass function of (x, y). as always, remember to state the range of x and y. then compute the joint probability mass function when (x, y) = (2,1). [hint: recall the formula for a conditional probability and note that we know the conditional probability and one of the marginal distributions].
(b) calculate the mean and variance of y. [hint: use the law of iterated expectations and variances].
(c) write down the formula for the joint (cumulative) distribution function of (x, y) using your result in part (a). as always, remember to state the relevant ranges of x and y. then compute the joint distribution function when x, y = (2,1). [hint: when writing down the joint distribution function, recall that the value of y must always be less than or equal to the value of x. if you are stuck on the second part, try making a table of the joint pmf of (x, y) up to the values x, y = (2,1)].
(d) write down the formula for the marginal probability mass function of y. as always, remember to state the range of y.
(e) note that y is less than x with zero probability so that, for example, p(x = 0, y = 1) = 0. use this and the fact that p (y=1) ≥ p(x=2, y=1) to determine whether x and y are independent. carefully show your argument.
Answers: 1
Mathematics, 21.06.2019 16:00, amylumey2005
Leo has b boxes of pencils. each box contains 6 pencils. he has a total of 42 pencils. the equation that represents this situation the value of b that makes the equation true the first one is b+6=42,6b=42,b=42+6,or 42b=6 the second one are 7,836 48
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Mathematics, 21.06.2019 19:00, milhai0627a
Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).
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Mathematics, 21.06.2019 20:10, dianacastro8298
Gexpressions: practice question 3 of 5 jackson wants to study the popularity of his music video by tracking the number of views the video gets on his website. the expression below represents the total number of views that jackson's video receives n days after he begins tracking the nu views, where b is the rate at which the number of views changes. alb)" select the statement that would accurately describe the effect of tripling a, the initial number of views before jackson beginst the rate at which the number of views changes, b, will triple. the total number of views the video has after n days, a(b)", will not change. the total number of days since jackson begins tracking views, n, will be reduced by one-third. the total number of views the video has after n days, alb)", will triple. submit
Answers: 3
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