Answer:
<em>H</em>₀: <em>μ₁ = μ₂= μ₃</em>
<em>Hₐ: </em>At least one of the means is different.
Step-by-step explanation:
Analysis of variance or ANOVA test is used to determine whether the means of different groups are similar or not.
The hypothesis of an ANOVA test for <em>n</em> homogeneous groups is:

In this case the researcher is testing whether the mean bone mineral density is different for the three different groups.
The hypothesis for this test can be defined as follows:
<em>H</em>₀: The mean bone mineral density is not different for the three different groups, i.e. <em>μ₁ = μ₂= μ₃</em>
<em>Hₐ: </em>The mean bone mineral density is different for the three different groups, i.e. at least one of the means is different.
[ ( x + 4 )( x + 5 ) + 4( x + 1 )( x + 5) - 5( x + 1 )( x + 4 ) ] / [( x + 1 )( x + 4)( x + 5 )] = ( x^2 + 9x + 20 + 4x^2 + 24x +20 - 5x^2 - 25x - 20) / [( x + 1 )( x + 4)( x + 5 )] =
( - 2x + 20 ) / [( x + 1 )( x + 4)( x + 5 )] = ( - 2)( x - 10) / [( x + 1 )( x + 4)( x + 5 )]
Answer:
The PMF of B is given by
P(B=0) = 0.7
P(B=1) = 0.16
P(B=2) = 0.08
P(B=3) = 0.04
P(B=4) = 0.02
Step-by-step explanation:
Let x denote P(B=1), we know that
P(B=0) = 1-0.3 = 0.7
P(B=1) = x
P(B=2) = x/2
P(B=3) = x/4
P(B=4) = x/8
Also, the probabilities should sum 1, thus
0.7+x+x/2+x/4+x/8 = 1
15x/8 = 0.3
x = 0.16
As a result, the PMF of B is given by
P(B=0) = 0.7
P(B=1) = 0.16
P(B=2) = 0.08
P(B=3) = 0.04
P(B=4) = 0.02