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(i) P(X <= 2, Y = 1) = P(X=0, Y=1) + P(X=1, Y=1) + P(X=2, Y=1)
= (0+1)/30 + (1+1)/30 + (2+1)/30 = 6/30 = 1/5.
(ii) P(X + Y = 4) = P(X=2, Y=2) + P(X=3, Y=1)
= (2+2)/30 + (3+1)/30 = 8/30 = 4/15.
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What is the Relationship between marginal and conditional and joint probabilities?
The joint probability of two discrete variables, X and Y isP(x, y) = Prob(X = x and Y = y) and it is defined for each ordered pair (x,y) in the event space.The conditional probability of X, given that Y is y is Prob[(X, Y) = (x, y)]/Prob(Y = y) or equivalently,Prob(X = x and Y = y)/Prob(Y = y)The marginal probability of X is simply the probability of X. It can be derived from the joint distribution by summing over all possible values of Y.
What is marginal probability?
Suppose you have two random variables, X and Y and their joint probability distribution function is f(x, y) over some appropriate domain. Then the marginal probability distribution of X, is the integral or sum of f(x, y) calculated over all possible values of Y.
What is exponential distribution?
The exponential distribution is a continuous probability distribution with probability density definded by: f(x) = ke-kx for x ≥ 0 and f(x) = 0 otherwise.
Discuss distribution function of mixed random variable?
In some situationsX is continuous but Y is discrete. For example, in a logistic regression, one may wish to predict the probability of a binary outcome Y conditional on the value of a continuously-distributed X. In this case, (X, Y) has neither a probability density function nor a probability mass function in the sense of the terms given above. On the other hand, a "mixed joint density" can be defined in either of two ways:Formally, fX,Y(x, y) is the probability density function of (X, Y) with respect to the product measure on the respective supports of X and Y. Either of these two decompositions can then be used to recover the joint cumulative distribution function:The definition generalizes to a mixture of arbitrary numbers of discrete and continuous random variables.
What is the Probability density function of Poisson distribution?
If a random variable X has a Poisson distribution with parameter l, then the probability that X takes the value x isPr(X = x) = lx*e-l/x! for x = 0, 1, 2, 3, ...
What is marginal probability function?
If f(x, y) is the joint probability distribution function of two random variables, X and Y, then the sum (or integral) of f(x, y) over all possible values of y is the marginal probability function of x. The definition can be extended analogously to joint and marginal distribution functions of more than 2 variables.
What is the Relationship between marginal and conditional and joint probabilities?
The joint probability of two discrete variables, X and Y isP(x, y) = Prob(X = x and Y = y) and it is defined for each ordered pair (x,y) in the event space.The conditional probability of X, given that Y is y is Prob[(X, Y) = (x, y)]/Prob(Y = y) or equivalently,Prob(X = x and Y = y)/Prob(Y = y)The marginal probability of X is simply the probability of X. It can be derived from the joint distribution by summing over all possible values of Y.
What is marginal probability?
Suppose you have two random variables, X and Y and their joint probability distribution function is f(x, y) over some appropriate domain. Then the marginal probability distribution of X, is the integral or sum of f(x, y) calculated over all possible values of Y.
What is joint probability function?
The joint probability function for two variables is a probability function whose domain is a subset of two dimensional space. The joint probability function for discrete random variables X and Y is given aspr(x, y) = pr(X = x and Y = y). If X and Y are independent random variables then this will equal pr(X =x)*pr(Y = y).For continuous variables, the joint funtion is defined analogously:f(x, y) = pr(X < x and Y < y).
What is exponential distribution?
The exponential distribution is a continuous probability distribution with probability density definded by: f(x) = ke-kx for x ≥ 0 and f(x) = 0 otherwise.
What is function joint?
The joint probability function for two variables is a probability function whose domain is a subset of two dimensional space. The joint probability function for discrete random variables X and Y is given aspr(x, y) = pr(X = x and Y = y). If X and Y are independent random variables then this will equal pr(X =x)*pr(Y = y).For continuous variables, the joint funtion is defined analogously:f(x, y) = pr(X < x and Y < y).
What discrete probability distribution can be approximated by a normal dsitribution?
If X has any discrete probability distribution then the sum of a number of observations for X will be normal.
What is joint probability?
Let X and Y be two random variables.Case (1) - Discrete CaseIf P(X = x) denotes the probability that the random variable X takes the value x, then the joint probability of X and Y is P(X = x and Y = y).Case (2) - Continuous CaseIf P(a < X < b) is the probability of the random variable X taking a value in the real interval (a, b), then the joint probability of X and Y is P(a < X< b and c < Y < d).Basically joint probability is the probability of two events happening (or not).
What is the Probability density function of Poisson distribution?
If a random variable X has a Poisson distribution with parameter l, then the probability that X takes the value x isPr(X = x) = lx*e-l/x! for x = 0, 1, 2, 3, ...
Discuss distribution function of mixed random variable?
In some situationsX is continuous but Y is discrete. For example, in a logistic regression, one may wish to predict the probability of a binary outcome Y conditional on the value of a continuously-distributed X. In this case, (X, Y) has neither a probability density function nor a probability mass function in the sense of the terms given above. On the other hand, a "mixed joint density" can be defined in either of two ways:Formally, fX,Y(x, y) is the probability density function of (X, Y) with respect to the product measure on the respective supports of X and Y. Either of these two decompositions can then be used to recover the joint cumulative distribution function:The definition generalizes to a mixture of arbitrary numbers of discrete and continuous random variables.
What is the probability of the specific value X if n 10 p 0.5 X and ge 7?
The probability will depend on the underlying distribution, which is not specified.
Standard normal distribution formula?
There is the normal probability density function (pdf) which is given in the attached link. The normal probability cumulative distribution function (cdf) is used to calculate probabilities, and there is no closed form equation for this. Many statistical programs have the cdf built in. Some references are given at the end of the link to find approximate cdf. The cdf, is usually written F(x) and the pdf f(x). F(x) is the integral of f(x) from minus infinity to x.
