Solution Pea plants contain two genes for seed color each of which may be Y for yellow seeds or G for green seeds

Solution Pea plants contain two genes for seed color each of which may be Y for yellow

genes for seed color each of which may be Y for yellow seeds or G for green seeds Plants that contain one of each

Solution Pea plants contain two genes for seed color each of which may be

Y for yellow seeds or G for green seeds Plants that contain one of each

Solution Pea plants contain two genes for seed color each of

Solution Pea plants contain two

Category: | General |

Words: | 1050 |

Amount: | $12 |

Writer: |

Paper instructions

Questions in the attachment and I think they fairly simple for stats experts.1)
Pea plants contain two genes for seed color, each of which may
be Y (for yellow seeds) or G (for green seeds). Plants that contain
one of each type of gene are called heterozygous. According to
the Mendelian theory of genetics, if two heterozygous plants are
crossed, each of their oFspring will have probability 0.75 of
having yellow seeds and probability 0.25 of having green seeds.
a)
Out of 100 oFspring of heterozygous plants, what is the
probability that more than 30 have green seeds? And, what
is the probability that between 30 and 35 inclusive have
green seeds?
[Hint: apply the normal distribution to the
binomial distribution and continuity correction]
2
Consider a fair coin.
a)
What is the probability of obtaining exactly 3 heads if a fair
coin is ±ipped 6 times?
b)
What is the probability of obtaining at least 4 head if a fair
coin is ±ipped 17 times.
3
Consider a sample
n
x
x
,...,
1
and let
c
x
y
i
i
?
?
for
,
,...,
2
,
1
n
i
?
where
c
is
some speci²ed number.
Give a general argument to show that the
sample variance of the
s
y
i
'
is identical to that of the
s
x
i
'
.
[Hint: How
are
y
and
x
related? When trying to ²nd a general argument to show
that the sample variance of the
s
y
i
'
is identical to that of the
s
x
i
'
,
use the variance formula
?
?
1
2
2
?
?
?
?
n
y
y
s
i
y
.]
4
A random variable
x
has an exponential distribution with parameter
?
;
that is, its density function is
( )
x
f x
e
?
?
?
?
for
x
> 0.
Express the interquartile range of the distribution in terms of the
parameter
?
.
[Hint: You will have to ²rst express the lower and upper
quartiles of the distribution in terms of the parameter
?
.]
1

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