a) there is no negative covid-19 test? b) exactly two covid-19 tests are negative? c) between two and four (inclusive) covid-19 tests are negative? (hi d) at most three covid-19 tests are negative? e) At least two covid-19 tests are negative? f) Exactly 3 covid-19 tests are positive? 2. Find: a) The expected number of the number of negative covid-19 tests. b) The standard deviation of the number of negative covid-19 tests.

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5. The probability distribution of the number of negative covid-19 tests after the first vaccine dose is
given below:
1
3
4
P(X = x) | 0.02
0.08
0.1
0.3
0.5
5.1. After the first vaccine dose, what is the probability that
a) there is no negative covid-19 test?
b) exactly two covid-19 tests are negative?
c) between two and four (inclusive) covid-19 tests are negative? (hint: P (2 < X < 4))
d) at most three covid-19 tests are negative?
e) At least two covid-19 tests are negative?
f) Exactly 3 covid-19 tests are positive?
5.2. Find:
a) The expected number of the number of negative covid-19 tests.
b) The standard deviation of the number of negative covid-19 tests.
Transcribed Image Text:5. The probability distribution of the number of negative covid-19 tests after the first vaccine dose is given below: 1 3 4 P(X = x) | 0.02 0.08 0.1 0.3 0.5 5.1. After the first vaccine dose, what is the probability that a) there is no negative covid-19 test? b) exactly two covid-19 tests are negative? c) between two and four (inclusive) covid-19 tests are negative? (hint: P (2 < X < 4)) d) at most three covid-19 tests are negative? e) At least two covid-19 tests are negative? f) Exactly 3 covid-19 tests are positive? 5.2. Find: a) The expected number of the number of negative covid-19 tests. b) The standard deviation of the number of negative covid-19 tests.
Expert Solution
Step 1

Let , X be the number of negative covid-19 test.

Since , the probability distribution of X is given by ,

X 0 1 2 3 4
P(x) 0.02 0.08 0.1 0.3 0.5

Our aim is to find the following : 

5.1 ) 

(a) P(X=0)

(b) P(X=2)

(c) P(2X4)

(d) P(X3)

(e) P(X2)

(f) P(X=3)

5.2 ) 

(a) E(X)

(b) Standard deviation 

 

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