Question

How probability and statistics are related?

Explain the role of probability in statistics according to the following rules:

Your posts must be written according to the following criteria:

• Must demonstrate your understanding of the topic.
• Connections between videos content and textbook content should be exhibited.
• Relate new information with personal experience.
• Discuss at a critical level – don’t just recite facts from your readings or discussion. Critical discussion includes your opinion of items mentioned, but also includes the reasons you hold that opinion, and why it may be inconsistent or consistent with what you’ve learned. Justify your reasoning with facts. How does what you’re presenting affect present and future situations?

Answer 1

unknown. 3.5. STATISTICAL (OR EMPIRICAL) PROBABILITY Oefinition. (VON MISES). If an experiment is performed repeatedly under essentially 87hamogene0us and identical conditions, then the limiting value of the ratio of the number of times the event occurs to the number of trials, as the number of trials becomes indefinitely large, is called the probability of happening of the event, it being assumed that the limit is finite and unique. Symbolically, if in N trials an event E happens M times, then the probability of the happening of E, denoted by P(E), is given by: ta = lim N (3.2) P(E) ... Na Remarks 1. Since in the relative frequency approach, the probability is obtained objectively by repetitive empirical observations, it is also known as 2. An experiment is unique and non-repeating only in the case of subjective probability. In other cases, there are a large number of experiments or trials to establish the chance of 'Empirical Probability'. Onb occurrence of an event. This is particulariy probability also, repeated experiments may be made to verify whether a deduction on the basis (31 so in case of empirical probability. In classical of certain axioms or undisputed laws is justified. Only after repeated trials it can be established 3 that the chance of head in a toss of a coin is 1/2. J. E. Kerrich conducted coin tossing experiment with 10 sets of 1,000 tosses each during his confinement in World War II. The number of heads found by him were: 502, 511, 497, 529, 504, 476, 507, 520, 504, 529. 5,079 This gives the probability of getting a head in a toss of a coin as 10,000 0-5079 Thus, the empirical probability approaches the classical probability as the number of trials becomes indefinitely large. 3.5-1. Limitations of Empirical Probability. (i) If an experiment is repeated a large number of times, the experimental conditions may not remain identical and homogeneous. (ii) The limit in (3-2) may not attain a unique value, however large N may be. Example 3-1. Whhat is the chance that a leap year selected at randon will contain 53 Sundays ? Solution. In a leap year (which consists of 366 days), there are 52 complete weeks and 2 days over. The following are the possible combinations for these two 'over' days: (1) Sunday and Monday, (ii) Monday and Tuesday, (iii) Tuesday and Wednesday, () Wednesday and Thursday, (v) Thursday and Friday, (vi) Friday and Saturday, and (vii) Saturday and Sunday. In order that a leap year selected at random should contain 53 Sundays, one of the Wo over days must be Sunday. Since out of the above 7 possibilities, 2, viz., (i) and (tii), are favourable to this event. Fer yaiideden 0 Latol Sab Required probability = trorm Find the nrohability that: