Find $P(1 le x < 3)$ if $X$ ~ $Binomial (100, 0.01)$
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Here's my approach:
$n = 100 , $ p = 0.01
To find $P(1 le x < 3)$, do I just find $P(X < 3) - P(1 le X)$?
probability probability-theory probability-distributions
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add a comment |
$begingroup$
Here's my approach:
$n = 100 , $ p = 0.01
To find $P(1 le x < 3)$, do I just find $P(X < 3) - P(1 le X)$?
probability probability-theory probability-distributions
$endgroup$
$begingroup$
no, you have to find $P(X<3)-P(X=0)$ which is $$P(Xleq 2)-P(X=0)=(P(X=0)+P(X=1)+P(X=2))-P(X=0)=P(X=1)+P(X=2)$$
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– Fakemistake
Dec 1 '18 at 7:22
add a comment |
$begingroup$
Here's my approach:
$n = 100 , $ p = 0.01
To find $P(1 le x < 3)$, do I just find $P(X < 3) - P(1 le X)$?
probability probability-theory probability-distributions
$endgroup$
Here's my approach:
$n = 100 , $ p = 0.01
To find $P(1 le x < 3)$, do I just find $P(X < 3) - P(1 le X)$?
probability probability-theory probability-distributions
probability probability-theory probability-distributions
edited Nov 29 '18 at 17:43
Yolanda Hui
asked Nov 29 '18 at 15:55
Yolanda HuiYolanda Hui
14810
14810
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no, you have to find $P(X<3)-P(X=0)$ which is $$P(Xleq 2)-P(X=0)=(P(X=0)+P(X=1)+P(X=2))-P(X=0)=P(X=1)+P(X=2)$$
$endgroup$
– Fakemistake
Dec 1 '18 at 7:22
add a comment |
$begingroup$
no, you have to find $P(X<3)-P(X=0)$ which is $$P(Xleq 2)-P(X=0)=(P(X=0)+P(X=1)+P(X=2))-P(X=0)=P(X=1)+P(X=2)$$
$endgroup$
– Fakemistake
Dec 1 '18 at 7:22
$begingroup$
no, you have to find $P(X<3)-P(X=0)$ which is $$P(Xleq 2)-P(X=0)=(P(X=0)+P(X=1)+P(X=2))-P(X=0)=P(X=1)+P(X=2)$$
$endgroup$
– Fakemistake
Dec 1 '18 at 7:22
$begingroup$
no, you have to find $P(X<3)-P(X=0)$ which is $$P(Xleq 2)-P(X=0)=(P(X=0)+P(X=1)+P(X=2))-P(X=0)=P(X=1)+P(X=2)$$
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– Fakemistake
Dec 1 '18 at 7:22
add a comment |
2 Answers
2
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oldest
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$begingroup$
Hints
Notice that
$$P(X=k)=binom{100}{k}(0.01)^k(0.99)^{100-k}$$
and that
$$
P(1leq X<3)=P(X=1)+P(X=2).
$$
$endgroup$
add a comment |
$begingroup$
To find $P(1 le x < 3)$, you do $P(X < 3) - P(X<1)$ not $P(X < 3) - P(1 le X)$ because
$$P(X<3) = P(X=0) + P(X=1) + P(X=2)$$
$$P(X<1) = P(X=0)$$
$$P(1 le X) = P(X=1) + P(X=2) + P(X=3) + P(X=4) + ... + P(X=100)$$
$$therefore, P(X < 3) - P(X<1) = P(X=1) + P(X=2)$$
and $P(X < 3) - P(1 le X) < 0$ which is impossible if $P(X < 3) - P(1 le X)$ is equal to the probability of some event which you guessed is $P(1 le X < 3) = P(X < 3) - P(1 le X)$
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Yeah thats a typo, thanks.
$endgroup$
– Yolanda Hui
Dec 1 '18 at 10:04
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hints
Notice that
$$P(X=k)=binom{100}{k}(0.01)^k(0.99)^{100-k}$$
and that
$$
P(1leq X<3)=P(X=1)+P(X=2).
$$
$endgroup$
add a comment |
$begingroup$
Hints
Notice that
$$P(X=k)=binom{100}{k}(0.01)^k(0.99)^{100-k}$$
and that
$$
P(1leq X<3)=P(X=1)+P(X=2).
$$
$endgroup$
add a comment |
$begingroup$
Hints
Notice that
$$P(X=k)=binom{100}{k}(0.01)^k(0.99)^{100-k}$$
and that
$$
P(1leq X<3)=P(X=1)+P(X=2).
$$
$endgroup$
Hints
Notice that
$$P(X=k)=binom{100}{k}(0.01)^k(0.99)^{100-k}$$
and that
$$
P(1leq X<3)=P(X=1)+P(X=2).
$$
edited Dec 1 '18 at 4:49
farruhota
19.7k2738
19.7k2738
answered Nov 29 '18 at 16:04
Foobaz JohnFoobaz John
21.6k41352
21.6k41352
add a comment |
add a comment |
$begingroup$
To find $P(1 le x < 3)$, you do $P(X < 3) - P(X<1)$ not $P(X < 3) - P(1 le X)$ because
$$P(X<3) = P(X=0) + P(X=1) + P(X=2)$$
$$P(X<1) = P(X=0)$$
$$P(1 le X) = P(X=1) + P(X=2) + P(X=3) + P(X=4) + ... + P(X=100)$$
$$therefore, P(X < 3) - P(X<1) = P(X=1) + P(X=2)$$
and $P(X < 3) - P(1 le X) < 0$ which is impossible if $P(X < 3) - P(1 le X)$ is equal to the probability of some event which you guessed is $P(1 le X < 3) = P(X < 3) - P(1 le X)$
$endgroup$
$begingroup$
Yeah thats a typo, thanks.
$endgroup$
– Yolanda Hui
Dec 1 '18 at 10:04
add a comment |
$begingroup$
To find $P(1 le x < 3)$, you do $P(X < 3) - P(X<1)$ not $P(X < 3) - P(1 le X)$ because
$$P(X<3) = P(X=0) + P(X=1) + P(X=2)$$
$$P(X<1) = P(X=0)$$
$$P(1 le X) = P(X=1) + P(X=2) + P(X=3) + P(X=4) + ... + P(X=100)$$
$$therefore, P(X < 3) - P(X<1) = P(X=1) + P(X=2)$$
and $P(X < 3) - P(1 le X) < 0$ which is impossible if $P(X < 3) - P(1 le X)$ is equal to the probability of some event which you guessed is $P(1 le X < 3) = P(X < 3) - P(1 le X)$
$endgroup$
$begingroup$
Yeah thats a typo, thanks.
$endgroup$
– Yolanda Hui
Dec 1 '18 at 10:04
add a comment |
$begingroup$
To find $P(1 le x < 3)$, you do $P(X < 3) - P(X<1)$ not $P(X < 3) - P(1 le X)$ because
$$P(X<3) = P(X=0) + P(X=1) + P(X=2)$$
$$P(X<1) = P(X=0)$$
$$P(1 le X) = P(X=1) + P(X=2) + P(X=3) + P(X=4) + ... + P(X=100)$$
$$therefore, P(X < 3) - P(X<1) = P(X=1) + P(X=2)$$
and $P(X < 3) - P(1 le X) < 0$ which is impossible if $P(X < 3) - P(1 le X)$ is equal to the probability of some event which you guessed is $P(1 le X < 3) = P(X < 3) - P(1 le X)$
$endgroup$
To find $P(1 le x < 3)$, you do $P(X < 3) - P(X<1)$ not $P(X < 3) - P(1 le X)$ because
$$P(X<3) = P(X=0) + P(X=1) + P(X=2)$$
$$P(X<1) = P(X=0)$$
$$P(1 le X) = P(X=1) + P(X=2) + P(X=3) + P(X=4) + ... + P(X=100)$$
$$therefore, P(X < 3) - P(X<1) = P(X=1) + P(X=2)$$
and $P(X < 3) - P(1 le X) < 0$ which is impossible if $P(X < 3) - P(1 le X)$ is equal to the probability of some event which you guessed is $P(1 le X < 3) = P(X < 3) - P(1 le X)$
answered Dec 1 '18 at 2:33
user198044
$begingroup$
Yeah thats a typo, thanks.
$endgroup$
– Yolanda Hui
Dec 1 '18 at 10:04
add a comment |
$begingroup$
Yeah thats a typo, thanks.
$endgroup$
– Yolanda Hui
Dec 1 '18 at 10:04
$begingroup$
Yeah thats a typo, thanks.
$endgroup$
– Yolanda Hui
Dec 1 '18 at 10:04
$begingroup$
Yeah thats a typo, thanks.
$endgroup$
– Yolanda Hui
Dec 1 '18 at 10:04
add a comment |
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$begingroup$
no, you have to find $P(X<3)-P(X=0)$ which is $$P(Xleq 2)-P(X=0)=(P(X=0)+P(X=1)+P(X=2))-P(X=0)=P(X=1)+P(X=2)$$
$endgroup$
– Fakemistake
Dec 1 '18 at 7:22