Q.2 Epilepsy is a chronic neurological disorder characterized by recurrent seizures. A large proportion of people with epilepsy do not have seizure control even with the best available medications. The following table gives the distribution of the number of seizures per year for a sample of 500 epilepsy patients who are using the same medication: # of seizure per year Frequency (# of 0 1 2 3 4 325 108 35 21 11 patients) Let Y be the number of seizures per year for a randomly chosen patient in this group. (a) Find the probability mass function of Y. (b) Find cumulative distribution function (cdf) and sketch it. (c) Find (i) measure of skewness (ẞ₁) and (ii) measure of kurtosis (ẞ2). (d) Compute P(Y ≥ 4). (e) Find moment generating function (mgf). (f) Find E(Y3) and V(Y + 3).
Q.2 Epilepsy is a chronic neurological disorder characterized by recurrent seizures. A large proportion of people with epilepsy do not have seizure control even with the best available medications. The following table gives the distribution of the number of seizures per year for a sample of 500 epilepsy patients who are using the same medication: # of seizure per year Frequency (# of 0 1 2 3 4 325 108 35 21 11 patients) Let Y be the number of seizures per year for a randomly chosen patient in this group. (a) Find the probability mass function of Y. (b) Find cumulative distribution function (cdf) and sketch it. (c) Find (i) measure of skewness (ẞ₁) and (ii) measure of kurtosis (ẞ2). (d) Compute P(Y ≥ 4). (e) Find moment generating function (mgf). (f) Find E(Y3) and V(Y + 3).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Q.2 Epilepsy is a chronic neurological disorder characterized by recurrent
seizures. A large proportion of people with epilepsy do not have seizure
control even with the best available medications. The following table gives
the distribution of the number of seizures per year for a sample of 500
epilepsy patients who are using the same medication:
# of seizure per year
Frequency (# of
0
1
2
3
4
325
108
35
21
11
patients)
Let Y be the number of seizures per year for a randomly chosen patient in
this group.
(a) Find the probability mass function of Y.
(b) Find cumulative distribution function (cdf) and sketch it.
(c) Find (i) measure of skewness (ẞ₁) and (ii) measure of kurtosis (ẞ2).
(d) Compute P(Y ≥ 4).
(e) Find moment generating function (mgf).
(f) Find E(Y3) and V(Y + 3).
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