Given: •pk denotes the probability that the number of claims equals k for k= 0,1,2,... •pn/pm=m!/...
Given:
•pk denotes the probability that the number of claims equals k for k= 0,1,2,...
•pn/pm=m!/n!, m≥0, n≥0
Using the corresponding zero-modified claim count distribution with P0M= 0.1, calculate P1M
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Given: •pk denotes the probability that the number of claims equals k for k= 0,1,2,... •pn/pm=m!/...
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer.
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer. a. Find the constant k. b. Find the expected value M(S) = E(esX) as a function of the real numbers s. Compare the values of the derivative of this function M'(0) at 0 and the expected value of a random variable having the probability function above. c. What distribution has probability function f(x)? Let X1, X2 be independent random variables both...
The annual frequency of claims against a single policy in a certain portfolio follows the distrib...
The annual frequency of claims against a single policy in a certain portfolio follows the distribution: P(N-0) 0.6, P(N-1) 0.25, P(N-2)-0.10, P(N-3) 0.0:5 There are 900 policies in this portfolio. Current staffing levels can handle as many as 580 claims against this portfolio in a year. If the annual claim count exceeds 580, then additional help wll be hired. The number of claims against different policies are independent. Calculate the probability that current staffing levels are adequate for next year....
15 Consider a block of N-10000 risk units j. each distribution of claims of compound mixed Poisso...
15 Consider a block of N-10000 risk units j. each distribution of claims of compound mixed Poisson type baring a same expected number n,-0.1 of claims. The standard Ht ion of the mixing variable q, of each risk uni js o 02. re, the joint claim size d.f. is approximated by a discrete monetary unit, say £1000, in ntble, where s, is the probability that the size of a claim as given in terms of some suitable Z, 16 s,...
1. This question is on probability a. Suppose that X is a normally distributed random variable,...
1. This question is on probability a. Suppose that X is a normally distributed random variable, where X N (M, o). Show that E [cºX f (x)] = cºu+20oʻE [ f (x + 002)] where f is a suitable function and 0 € R is a scalar. Hint: Write X = 1 +o0; 0~ N (0,1) and calculate the resulting integral b. Consider the probability density function X>0 p(x) = { Az exp (-1.2-2) 10 x < 0 (>0) is...
1. A mail-order computer business has six telephone lines. X denotes the number The probability mass...
1. A mail-order computer business has six telephone lines. X denotes the number The probability mass function of X is given of the lines in use at a specified time. in the accompanying table. 0 2 20 3 25 20 4 5 06 6 04 P(Xx) 10 .15 Find P(1< X <4) and P(X-2) b. E(X), Var(X) c. In a random sample of 10 randomly selected times, let Y be the number of the times that exactly two lines are...
Solve the LAST ONE INCLUDE ALL THE STEPS The force constant for the carbon monoxide molecule is 1,908 N m At 1,000 K what is the probability that the molecule will be found in the lowest excited state...
Solve the LAST ONE INCLUDE ALL
THE STEPS
The force constant for the carbon monoxide molecule is 1,908 N m At 1,000 K what is the probability that the molecule will be found in the lowest excited state? At a given temperature the rotational states of molecules are distributed according to the Boltzmann distribution. Of the hydrogen molecules in the ground state estimate the ratio of the number in the ground rotational state to the number in the first excited...
Examination in probability theory and statistics Variant 9 1. Discrete distribution for X is given by...
Examination in probability theory and statistics Variant 9 1. Discrete distribution for X is given by the following table: Probability p ValueX Find distribution function fa) and median Me(0). Calculate mathematical expectation (the mean) M(x), 0.3 -10 0.4 10 0.2 20 0.1 40 variance (dispersion) Da, standard error ơ(X), asymmetry coefficient As(X) and excess Ex(X). 2. Calculate multiplier k. Find mode Mots, median Me(o), mathematical expectation (the mean) Mc) variance (dispersion) D(x) and standard error σ(x) for continuous distributions having...
10. A manager is responsible for n machines. In any given period, the probability that exactly...
10. A manager is responsible for n machines. In any given period, the probability that exactly k machines will break down is Tk> 0 (πΟΤ π1+π2+ π,-1), where k is any whole number between 0 and n: k=0, 1, 2, , n. The Tk are "true" probabilities but are known only to the manager. The manager must report these probabilities to the control authority. In the absence of any re ward or penalty, he might report some wrong probabilities Po,...
10. A manager is responsible for n machines. In any given period, the probability that exactly...
10. A manager is responsible for n machines. In any given period, the probability that exactly k machines will break down is Tk> 0 (πΟΤ π1+π2+ π,-1), where k is any whole number between 0 and n: k=0, 1, 2, , n. The Tk are "true" probabilities but are known only to the manager. The manager must report these probabilities to the control authority. In the absence of any re ward or penalty, he might report some wrong probabilities Po,...
Spring mass damper system with forced response, the forced system given by the equation For damping...
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
The annual frequency of claims against a single policy in a certain portfolio follows the distribution: P(N-0) 0.6, P(N-1) 0.25, P(N-2)-0.10, P(N-3) 0.0:5 There are 900 policies in this portfolio. Current staffing levels can handle as many as 580 claims against this portfolio in a year. If the annual claim count exceeds 580, then additional help wll be hired. The number of claims against different policies are independent. Calculate the probability that current staffing levels are adequate for next year....
15 Consider a block of N-10000 risk units j. each distribution of claims of compound mixed Poisson type baring a same expected number n,-0.1 of claims. The standard Ht ion of the mixing variable q, of each risk uni js o 02. re, the joint claim size d.f. is approximated by a discrete monetary unit, say £1000, in ntble, where s, is the probability that the size of a claim as given in terms of some suitable Z, 16 s,...
1. This question is on probability a. Suppose that X is a normally distributed random variable, where X N (M, o). Show that E [cºX f (x)] = cºu+20oʻE [ f (x + 002)] where f is a suitable function and 0 € R is a scalar. Hint: Write X = 1 +o0; 0~ N (0,1) and calculate the resulting integral b. Consider the probability density function X>0 p(x) = { Az exp (-1.2-2) 10 x < 0 (>0) is...
1. A mail-order computer business has six telephone lines. X denotes the number The probability mass function of X is given of the lines in use at a specified time. in the accompanying table. 0 2 20 3 25 20 4 5 06 6 04 P(Xx) 10 .15 Find P(1< X <4) and P(X-2) b. E(X), Var(X) c. In a random sample of 10 randomly selected times, let Y be the number of the times that exactly two lines are...
Solve the LAST ONE INCLUDE ALL
THE STEPS
The force constant for the carbon monoxide molecule is 1,908 N m At 1,000 K what is the probability that the molecule will be found in the lowest excited state? At a given temperature the rotational states of molecules are distributed according to the Boltzmann distribution. Of the hydrogen molecules in the ground state estimate the ratio of the number in the ground rotational state to the number in the first excited...
Examination in probability theory and statistics Variant 9 1. Discrete distribution for X is given by the following table: Probability p ValueX Find distribution function fa) and median Me(0). Calculate mathematical expectation (the mean) M(x), 0.3 -10 0.4 10 0.2 20 0.1 40 variance (dispersion) Da, standard error ơ(X), asymmetry coefficient As(X) and excess Ex(X). 2. Calculate multiplier k. Find mode Mots, median Me(o), mathematical expectation (the mean) Mc) variance (dispersion) D(x) and standard error σ(x) for continuous distributions having...
10. A manager is responsible for n machines. In any given period, the probability that exactly k machines will break down is Tk> 0 (πΟΤ π1+π2+ π,-1), where k is any whole number between 0 and n: k=0, 1, 2, , n. The Tk are "true" probabilities but are known only to the manager. The manager must report these probabilities to the control authority. In the absence of any re ward or penalty, he might report some wrong probabilities Po,...
10. A manager is responsible for n machines. In any given period, the probability that exactly k machines will break down is Tk> 0 (πΟΤ π1+π2+ π,-1), where k is any whole number between 0 and n: k=0, 1, 2, , n. The Tk are "true" probabilities but are known only to the manager. The manager must report these probabilities to the control authority. In the absence of any re ward or penalty, he might report some wrong probabilities Po,...
Spring mass damper system with forced response, the forced system given by the equation For damping factor:E-0.1 ; mass; m-| kg: stiffness of spring; k-100 Nm; f-| 00 N; ω Zun; initial condition: x (0)-2 cms; r(0) = 0. fsincot Task Marks 1. Write down the reduced equation into 2first orderns Hand written equations differential equations 2. Rearrange equation (1) with the following generalized equation 250, x+osinor calculations 3. Calculate the value of c calculations Hand calculations 4. Using the...
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