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caprisun1491
29.02.2020 •
Mathematics
A family has j children with probability pj , where p1 = .1, p2 = .25, p3 = .35, p4 = .3. A child from this family is randomly chosen. Given that the child is the eldest child in the family, find the conditional probability that the family has
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Ответ:
A) the conditional probability that the has only 1 child = 0.24
B) The conditional probability that the family has only 4 children = 0.18
Step-by-step explanation:
To answer the questions, we first start with defining each event. Let E be the event that the child selected is the oldest and let Fj be the event that the family has j children.
From this, we can deduce that the probability that the child is the oldest, given that there is j children is ; P(E | Fj ) = 1/j.
In addition, we know P(Fj ) = pj as given in the problem. In answering the 2 questions, we seek the probability P(Fj | E). Thus, by the Bayes’s formula;
P(Fj | E) = P(EFj )/P(E) which gives;
P(Fj | E) = {P(E | Fj )P(Fj )} / {Σ(4,i=1)P(E | Fj )P(Fj )}
= (1/j)/ Σ(4,i=1)(1/j)pj
= ((pj)/j) / {p1 + (p2)/2 + (p3)/3 +(p4)/4}
Therefore, the conditional probability that the family has only 1 child; P(F1 | E) = p1 / {p1 + (p2)/2 + (p3)/3 +(p4)/4} = 0.1/ (0.1 + (0.25/2) +(0.35/3) + (0.3/4) = 0.1/0.4167 = 0.24
The conditional probability that the family has only 4 children =
{(p4)/4} / {p1 + (p2)/2 + (p3)/3 +(p4)/4} = (0.3/4)/ (0.1 + (0.25/2) +(0.35/3) + (0.3/4) = 0.075/0.4167 = 0.18
Ответ:
y = 11.84x - 32.71
Step-by-step explanation:
Here, the given data points,
(−3,−70),(−1,−42),(1,−21),(2,−9),(4,14),
Let x represents the input value and y represents the output value,
So, the table that represents the given situation is,
x -3 -1 1 2 4
y -70 -42 -21 -9 14
By the above table,
Let the equation of the line is,
y = bx + a
Where,
n = number of data points = 5,
By substituting the values we get,
a = - 32.70547945 ≈ - 32.71,
b = 11.84246575 ≈ 11.84,
Hence, the equation of line would be,
y = 11.84x - 32.71