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Ms Skelhorne escaped with her baby when another family member smashed her bedroom window.
"The most callous thing was setting fire to the staircase," said Mr Bimpson. "How can you get out of a house when the staircase is on fire filled with black smoke and you cannot breathe? The main priority was getting the kids out but unfortunately time ran out for Francesca."
Ms Skelhorne, 36, clutching her teenage son's hand, wept copiously throughout the short press conference at Merseyside Police headquarters. She was anxious to display a large photograph of the photogenic child who had been looking forward to starting at a new nursery school.
She said: "She was burnt alive. That is what happened — somebody burnt her alive and we don't know what for.
"They have robbed us of the most gorgeous girl — she had so much to offer. She was a lovely singer and dancer.
"The kids are missing her. The baby is missing her. Christina is missing her — we are all missing her but we cannot have her back." Francesca, who was rescued from her upstairs bedroom by firefighters, died in Alder Hey Hospital on December 23
Ms Skelhorne said: "I sometimes wish she had died in the fire because of the three weeks she went through after that. She suffered like hell in hospital. She was trying to move her mouth. I knew she was not going to make it."
Two men, aged 45 and 43, have been arrested in connection with the investigation. They are on police bail.
Mr Bimpson said: "We are a normal loving family. All I can say is that my kids are a credit to the community, and I have done a lot of things for the local community. At the end of the day somebody is either jealous or mentally ill to have done that.
"One of us has been killed for no reason whatsoever. I cannot understand it. I have no problems with anyone."
Detective Superintendent David Kelly, who has taken over the murder inquiry, said that there does not appear to be any obvious motive for the attack.
He said: "There is no reason we can find why somebody would want to attack a house with two sleeping adults and four children.
"A little girl was killed as she was looking forward to Christmas.
"Her family are devastated and if you have any information, I would urge you to search you consciences and come forward so we can bring the offender or offenders to justice."
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