N
ntalwar
Member
Hi,
I am really struggling with understanding how are the values of the probabilities obtained in questions relating to finding the probability if an accumulation of a sum will be more or less than a given value. For example, in the exam-style question 2, how is P(Z > 0.547) = 0.292? I see the value of ᶲ (0.55) = 0.70884 (which is the nearest value for x = 0.547) in the tables on page 160 of the actuarial tables.
Q&A Bank Part 4 Question 4.9 (asking if the accumulated value will be more than £230) - how is P(Z > 1.165) = 1 - 0.87799? The nearest value to 1.165 in the tables is 1.17 and ᶲ (1.17) = 0.87900.
Basically, I want to find out how do you calculate ᶲ (x) for a given x. I know that it is a complex calculation involving the erf function, but why do the course notes/Q&A Bank then have exact values in the calculations instead of just nearest values from the tables?
Also, what is the effect of changing signs within the brackets, i.e. changing < to >, or <= to >=?
Would appreciate if I can get an explanation of above? This is really troubling me as I can understand the probability distribution function of a standard normal distribution but cannot see how the course notes are calculating exact values when the web (wikipedia etc) describe calculating probabilities as somewhat impossible except with a computer program.
I am really struggling with understanding how are the values of the probabilities obtained in questions relating to finding the probability if an accumulation of a sum will be more or less than a given value. For example, in the exam-style question 2, how is P(Z > 0.547) = 0.292? I see the value of ᶲ (0.55) = 0.70884 (which is the nearest value for x = 0.547) in the tables on page 160 of the actuarial tables.
Q&A Bank Part 4 Question 4.9 (asking if the accumulated value will be more than £230) - how is P(Z > 1.165) = 1 - 0.87799? The nearest value to 1.165 in the tables is 1.17 and ᶲ (1.17) = 0.87900.
Basically, I want to find out how do you calculate ᶲ (x) for a given x. I know that it is a complex calculation involving the erf function, but why do the course notes/Q&A Bank then have exact values in the calculations instead of just nearest values from the tables?
Also, what is the effect of changing signs within the brackets, i.e. changing < to >, or <= to >=?
Would appreciate if I can get an explanation of above? This is really troubling me as I can understand the probability distribution function of a standard normal distribution but cannot see how the course notes are calculating exact values when the web (wikipedia etc) describe calculating probabilities as somewhat impossible except with a computer program.