3 The moment generating function of a random variable Xis(1-2t)^(-3) .(i) Find the mean and variance of X.[5] (ii) X, and X, are two independent observations of X. Find [(X_1+X_2)^3] .[4] 相关知识点: 试题来源: 解析 (I) M'(t)=6(1-2t)^(-4) Alternative M'(0)...
(i)Show that the probability generating function of a random variable with the distribution B(n, p)is(1-p+pt)^n . [3] 相关知识点: 试题来源: 解析 r=0 ∑(pt)""C,(1-p)"-" r=0 =(1-p+pt)^n AGUse∑t'P(R=r) and binomial probabilities Indicate correct final term Collect p"...
Before we define the moment generating function, we begin by setting the stage with notation and definitions. We letXbe adiscrete random variable. This random variable has the probability mass functionf(x). The sample space that we are working with will be denoted byS. Rather than calculating ...
CumulantGeneratingFunction(X,t,options) CGF(X,t,options) Parameters X - algebraic; random variable or distribution t - algebraic; point options - (optional) equation of the formnumeric=value; specifies options for computing the cumulant generating function of a random variable ...
Moment Generating Function:The moment generating function or mgf of a random variable is a special function of a random variable. It is used to find moments of a certain random variable. The mgf has different useful properties. Suppose {eq}X {/eq} be a random variable then the ...
Find and simplify an expression for the probability generating function of the random variable xmhrcx-B(4,1/3) 相关知识点: 试题来源: 解析 P(x=x)=(4/x)(2/3)^x(1/3)^x This can be G(t)=(2/3)^4+4(2/3)^5(1/3)^2t+6(2/3)^2(1/3)^2t^2 recognised as a binomial ...
Another important result is that the moment generating function uniquely determines the distribution. That is, there exists a one-to-one correspondence between the moment generating function and the distribution function of a random variable. Example 2.46 Sums of Independent Binomial Random Variables If...
百度试题 结果1 题目 The probability generating function of the discrete random variable Xis given by:G_X=k(1+2t+3t^2)^3Find P(X= 2). 相关知识点: 试题来源: 解析 7/(72) 反馈 收藏
The Probability generating function of a random variable which has Generalized Polya Eggenberger Distribution of the second kind ( GPED 2 ) is obtained. The probability density function of the range R , in random sampling from a uniform distribution on ( k, l ) and exponential distribution with...
The moment generating function has great practical relevance because: it can be used to easily derivemoments; its derivatives at zero are equal to the moments of the random variable; a probability distribution is uniquely determined by its mgf. ...